Previous Quantum Matter/Condensed Matter Seminar schedule information and video links can be found here.
As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place Wednesdays from 10:30 – 12:00pm on Zoom. The Condensed Matter/Math Seminar will take place on Thursdays from 10:30 – 12:00pm on Zoom. In addition to the Quantum Matter seminar, the CMSA will also be hosting a related seminar series on a Strongly Correlated Quantum Materials and High-Temperature Superconductors. Please email the seminar organizer to obtain a link.
The schedules for both seminars will be updated below as speakers are confirmed:
Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.
Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.
Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.
Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry. Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.
Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.
Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.
Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.
Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the `side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field. This work is based on arxiv: 2201.11681
Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv 2201.00903.
Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.
Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.
Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).
Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information- theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem. The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories. Our techniques generalize to other RG flow equations beyond Polchinski’s.
Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.
4/7/2022
Jung Hoon Han (Sungkyunkwan University, Suwon, South Korea)
Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.
References: [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021) [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022) [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation. [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.
Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)
4/20/2022 11:30–1:00 pm ET
Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)
Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.
Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.
Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.
Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.
Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.
Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045
Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+ → 3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.
Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.
Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.
Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory. Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.
Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.
[1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021) [2] V. Crepel and L. Fu, arXiv:2103.12060 [3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)
Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.
Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.
Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation. I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups. In particular, I expand on a subtlety first flagged by Greaves-Thomas.
Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.
Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.
Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.
Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion. For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.
Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.
Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases. We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006. Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples. After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.
Abstract: For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.
Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature. I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.
Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:
[1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155) [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL) [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)
Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.
Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).
Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.
Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems. Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]
Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.
Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.
Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.
Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators. References: [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015) [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017) [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017) [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)
7/28/2021
Max Metlitski (MIT)
Title: Boundary criticality of the O(N) model in d = 3 critically revisited.
Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry. Based on arXiv:2009.05119.
Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.
8/4/2021
Nathan Benjamin (Princeton & Caltech)
Title: Harmonic analysis of 2d CFT partition functions
Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.
8/5/2021
Hans-Werner Hammer (TU Darmstadt)
Title: Un-nuclear physics: conformal symmetry in nuclear reactions
Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.
8/11/2021
Piers Coleman (Rutgers)
Title: Order Fractionalization*
Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).
8/12/2012
Beni Yoshida (Perimeter Institute)
Title: On the firewall puzzle
Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.
8/18/2021
Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)
Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
8/19/2021
Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)
Title: “Probing the Standard Model of Particle Physics Using the Muon Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
8/25/2021
Hitoshi Murayama (UC Berkely & IPMU)
Title: Some Exact Results in QCD-like and Chiral Gauge Theories
Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.
Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”
I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.
Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.
Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.
2/3/2020
Philip Phillips (University of Illinois Urbana-Champaign)
Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates. [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).
Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).
Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
[1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789 [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523
Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.
Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.
Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.
Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics. I will start with the conceptual origin of this model as requested by the organizer. Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds. In the end, I will mention lattice models that generalize the Haah codes in two directions: general three manifolds and more than two qubits per site.
If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum. New lattice models in fracton physics raise an interesting question: what kinds of quantum field theories are they approximating if their continuous limits exist? Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.
Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.
Abstract: We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories. Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics. In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls. This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.
Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.
Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.
Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening. In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N. Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations. I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion. This talk is based on joint work with R. Dempsey and I. Klebanov.
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.
Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.
Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.
Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.
Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.
Title: Chiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.
TitleNon-abelian bosonization in two and three spatial dimensions and some applications Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter. These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states. After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries. I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.
Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.
5/6/2021
Weslei Bernardino Fontana (Boston University & Estadual)
Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.
Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.
Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].
Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided. The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory of ghost fermions that carry neither spin nor charge. I will also describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.
Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.
Abstract: We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The holomorphic bc ghost system realizes all the exotic consistent anomalies.
Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553
Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.
Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems. Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations. Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment. The measures are based off of the entanglement of purification and the reflected entropy popular among holography. For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases. We conclude with a few remarks regarding applications to 2D phases.
Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice, with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.
Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.
Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action. We find these instantons in all spacetime dimensions, for AdS and dS. Many can be written in closed form and are quadratically stable. In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes. We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.
Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions. Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.
Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.
Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.
Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.
10/21/2020
Oleg Dubinkin (University of Illinois at Urbana–Champaign)
Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.
Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains. These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.
Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.
Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.
Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.
Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond. Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.
[1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003) [2] M. Hashimoto et al., Nature Physics 10, 483 (2014) [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys. [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993) [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995) [6] A. Lanzara et al., Nature 412, 510 (2001) [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004) [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004) [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995) [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996) [11] A.G. Loeser et al., Science 273, 325 (1996) [12] S. Chen et al., Science, 366, 6469 (2019) [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004) [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012) [15] Yu He et al., Science, 362, 62 (Oct. 2018) [16] Z. Chen, Y. Wang et al., preprint, 2020
Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
11/12/2020
Chandra Varma (University of California, Riverside)
This talk is organized as follows: 1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates. 2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations. 3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments. 4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.
Time permitting, (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity. (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors. (iii) Problems.
11/18/2020
Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)
Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.
11/19/2020
Eduardo Fradkin (University of Illinois at Urbana-Champaign)
Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.
Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.
Abstract: I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.
Abstract: Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics. I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter. How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!) remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
Abstract: The temperature versus doping phase diagram of the cuprate high-T_{c} superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa_{2}Cu_{3}O_{y }[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr_{2}CuO_{2}Cl_{2 }[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon. [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa_{2}Cu_{3}O_{y},” Nature Phys. 13, 250 (2017).
[2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr_{2}CuO_{2}Cl_{2},” Preprint at https://arxiv.org/abs/2008.06516 .
Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.
Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
The CMSA will host a weekly seminar running through 2020-21, where researchers from all areas of computer science present modern frontiers in computer science to the general mathematical audience. Talks shall be accessible to anyone with a good mathematical background; no domain-specific background is required. The seminar will run weekly on Tuesday 11:30 am ET.
Title: Naturalness and muon anomalous magnetic moment
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
Previous Quantum Matter/Condensed Matter Seminar schedule information and video links can be found here.
As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place Wednesdays from 10:30 – 12:00pm on Zoom. The Condensed Matter/Math Seminar will take place on Thursdays from 10:30 – 12:00pm on Zoom. In addition to the Quantum Matter seminar, the CMSA will also be hosting a related seminar series on a Strongly Correlated Quantum Materials and High-Temperature Superconductors. Please email the seminar organizer to obtain a link.
The schedules for both seminars will be updated below as speakers are confirmed:
Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.
Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.
Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.
Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry. Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.
Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.
Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.
Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.
Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the `side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field. This work is based on arxiv: 2201.11681
Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv 2201.00903.
Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.
Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.
Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).
Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information- theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem. The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories. Our techniques generalize to other RG flow equations beyond Polchinski’s.
Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.
4/7/2022
Jung Hoon Han (Sungkyunkwan University, Suwon, South Korea)
Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.
References: [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021) [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022) [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation. [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.
Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)
4/20/2022 11:30–1:00 pm ET
Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)
Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.
Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.
Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.
Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.
Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.
Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045
Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+ → 3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.
Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.
Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.
Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory. Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.
Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.
[1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021) [2] V. Crepel and L. Fu, arXiv:2103.12060 [3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)
Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.
Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.
Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation. I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups. In particular, I expand on a subtlety first flagged by Greaves-Thomas.
Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.
Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.
Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.
Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion. For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.
Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.
Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases. We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006. Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples. After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.
Abstract: For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.
Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature. I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.
Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:
[1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155) [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL) [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)
Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.
Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).
Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.
Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems. Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]
Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.
Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.
Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.
Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators. References: [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015) [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017) [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017) [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)
7/28/2021
Max Metlitski (MIT)
Title: Boundary criticality of the O(N) model in d = 3 critically revisited.
Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry. Based on arXiv:2009.05119.
Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.
8/4/2021
Nathan Benjamin (Princeton & Caltech)
Title: Harmonic analysis of 2d CFT partition functions
Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.
8/5/2021
Hans-Werner Hammer (TU Darmstadt)
Title: Un-nuclear physics: conformal symmetry in nuclear reactions
Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.
8/11/2021
Piers Coleman (Rutgers)
Title: Order Fractionalization*
Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).
8/12/2012
Beni Yoshida (Perimeter Institute)
Title: On the firewall puzzle
Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.
8/18/2021
Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)
Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
8/19/2021
Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)
Title: “Probing the Standard Model of Particle Physics Using the Muon Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
8/25/2021
Hitoshi Murayama (UC Berkely & IPMU)
Title: Some Exact Results in QCD-like and Chiral Gauge Theories
Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.
Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”
I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.
Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.
Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.
2/3/2020
Philip Phillips (University of Illinois Urbana-Champaign)
Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates. [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).
Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).
Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
[1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789 [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523
Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.
Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.
Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.
Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics. I will start with the conceptual origin of this model as requested by the organizer. Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds. In the end, I will mention lattice models that generalize the Haah codes in two directions: general three manifolds and more than two qubits per site.
If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum. New lattice models in fracton physics raise an interesting question: what kinds of quantum field theories are they approximating if their continuous limits exist? Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.
Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.
Abstract: We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories. Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics. In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls. This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.
Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.
Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.
Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening. In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N. Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations. I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion. This talk is based on joint work with R. Dempsey and I. Klebanov.
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.
Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.
Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.
Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.
Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.
Title: Chiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.
TitleNon-abelian bosonization in two and three spatial dimensions and some applications Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter. These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states. After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries. I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.
Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.
5/6/2021
Weslei Bernardino Fontana (Boston University & Estadual)
Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.
Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.
Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].
Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided. The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory of ghost fermions that carry neither spin nor charge. I will also describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.
Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.
Abstract: We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The holomorphic bc ghost system realizes all the exotic consistent anomalies.
Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553
Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.
Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems. Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations. Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment. The measures are based off of the entanglement of purification and the reflected entropy popular among holography. For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases. We conclude with a few remarks regarding applications to 2D phases.
Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice, with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.
Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.
Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action. We find these instantons in all spacetime dimensions, for AdS and dS. Many can be written in closed form and are quadratically stable. In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes. We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.
Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions. Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.
Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.
Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.
Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.
10/21/2020
Oleg Dubinkin (University of Illinois at Urbana–Champaign)
Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.
Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains. These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.
Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.
Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.
Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.
Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond. Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.
[1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003) [2] M. Hashimoto et al., Nature Physics 10, 483 (2014) [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys. [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993) [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995) [6] A. Lanzara et al., Nature 412, 510 (2001) [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004) [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004) [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995) [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996) [11] A.G. Loeser et al., Science 273, 325 (1996) [12] S. Chen et al., Science, 366, 6469 (2019) [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004) [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012) [15] Yu He et al., Science, 362, 62 (Oct. 2018) [16] Z. Chen, Y. Wang et al., preprint, 2020
Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
11/12/2020
Chandra Varma (University of California, Riverside)
This talk is organized as follows: 1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates. 2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations. 3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments. 4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.
Time permitting, (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity. (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors. (iii) Problems.
11/18/2020
Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)
Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.
11/19/2020
Eduardo Fradkin (University of Illinois at Urbana-Champaign)
Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.
Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.
Abstract: I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.
Abstract: Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics. I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter. How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!) remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
Abstract: The temperature versus doping phase diagram of the cuprate high-T_{c} superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa_{2}Cu_{3}O_{y }[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr_{2}CuO_{2}Cl_{2 }[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon. [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa_{2}Cu_{3}O_{y},” Nature Phys. 13, 250 (2017).
[2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr_{2}CuO_{2}Cl_{2},” Preprint at https://arxiv.org/abs/2008.06516 .
Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.
Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
The CMSA will host a weekly seminar running through 2020-21, where researchers from all areas of computer science present modern frontiers in computer science to the general mathematical audience. Talks shall be accessible to anyone with a good mathematical background; no domain-specific background is required. The seminar will run weekly on Tuesday 11:30 am ET.
Title: Naturalness and muon anomalous magnetic moment
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
Previous Quantum Matter/Condensed Matter Seminar schedule information and video links can be found here.
As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place Wednesdays from 10:30 – 12:00pm on Zoom. The Condensed Matter/Math Seminar will take place on Thursdays from 10:30 – 12:00pm on Zoom. In addition to the Quantum Matter seminar, the CMSA will also be hosting a related seminar series on a Strongly Correlated Quantum Materials and High-Temperature Superconductors. Please email the seminar organizer to obtain a link.
The schedules for both seminars will be updated below as speakers are confirmed:
Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.
Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.
Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.
Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry. Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.
Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.
Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.
Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.
Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the `side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field. This work is based on arxiv: 2201.11681
Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv 2201.00903.
Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.
Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.
Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).
Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information- theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem. The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories. Our techniques generalize to other RG flow equations beyond Polchinski’s.
Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.
4/7/2022
Jung Hoon Han (Sungkyunkwan University, Suwon, South Korea)
Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.
References: [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021) [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022) [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation. [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.
Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)
4/20/2022 11:30–1:00 pm ET
Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)
Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.
Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.
Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.
Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.
Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.
Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045
Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+ → 3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.
Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.
Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.
Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory. Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.
Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.
[1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021) [2] V. Crepel and L. Fu, arXiv:2103.12060 [3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)
Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.
Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.
Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation. I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups. In particular, I expand on a subtlety first flagged by Greaves-Thomas.
Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.
Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.
Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.
Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion. For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.
Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.
Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases. We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006. Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples. After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.
Abstract: For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.
Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature. I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.
Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:
[1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155) [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL) [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)
Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.
Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).
Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.
Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems. Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]
Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.
Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.
Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.
Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators. References: [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015) [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017) [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017) [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)
7/28/2021
Max Metlitski (MIT)
Title: Boundary criticality of the O(N) model in d = 3 critically revisited.
Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry. Based on arXiv:2009.05119.
Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.
8/4/2021
Nathan Benjamin (Princeton & Caltech)
Title: Harmonic analysis of 2d CFT partition functions
Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.
8/5/2021
Hans-Werner Hammer (TU Darmstadt)
Title: Un-nuclear physics: conformal symmetry in nuclear reactions
Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.
8/11/2021
Piers Coleman (Rutgers)
Title: Order Fractionalization*
Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).
8/12/2012
Beni Yoshida (Perimeter Institute)
Title: On the firewall puzzle
Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.
8/18/2021
Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)
Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
8/19/2021
Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)
Title: “Probing the Standard Model of Particle Physics Using the Muon Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
8/25/2021
Hitoshi Murayama (UC Berkely & IPMU)
Title: Some Exact Results in QCD-like and Chiral Gauge Theories
Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.
Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”
I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.
Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.
Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.
2/3/2020
Philip Phillips (University of Illinois Urbana-Champaign)
Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates. [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).
Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).
Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
[1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789 [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523
Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.
Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.
Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.
Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics. I will start with the conceptual origin of this model as requested by the organizer. Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds. In the end, I will mention lattice models that generalize the Haah codes in two directions: general three manifolds and more than two qubits per site.
If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum. New lattice models in fracton physics raise an interesting question: what kinds of quantum field theories are they approximating if their continuous limits exist? Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.
Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.
Abstract: We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories. Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics. In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls. This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.
Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.
Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.
Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening. In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N. Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations. I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion. This talk is based on joint work with R. Dempsey and I. Klebanov.
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.
Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.
Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.
Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.
Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.
Title: Chiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.
TitleNon-abelian bosonization in two and three spatial dimensions and some applications Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter. These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states. After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries. I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.
Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.
5/6/2021
Weslei Bernardino Fontana (Boston University & Estadual)
Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.
Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.
Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].
Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided. The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory of ghost fermions that carry neither spin nor charge. I will also describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.
Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.
Abstract: We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The holomorphic bc ghost system realizes all the exotic consistent anomalies.
Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553
Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.
Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems. Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations. Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment. The measures are based off of the entanglement of purification and the reflected entropy popular among holography. For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases. We conclude with a few remarks regarding applications to 2D phases.
Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice, with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.
Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.
Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action. We find these instantons in all spacetime dimensions, for AdS and dS. Many can be written in closed form and are quadratically stable. In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes. We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.
Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions. Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.
Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.
Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.
Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.
10/21/2020
Oleg Dubinkin (University of Illinois at Urbana–Champaign)
Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.
Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains. These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.
Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.
Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.
Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.
Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond. Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.
[1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003) [2] M. Hashimoto et al., Nature Physics 10, 483 (2014) [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys. [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993) [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995) [6] A. Lanzara et al., Nature 412, 510 (2001) [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004) [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004) [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995) [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996) [11] A.G. Loeser et al., Science 273, 325 (1996) [12] S. Chen et al., Science, 366, 6469 (2019) [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004) [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012) [15] Yu He et al., Science, 362, 62 (Oct. 2018) [16] Z. Chen, Y. Wang et al., preprint, 2020
Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
11/12/2020
Chandra Varma (University of California, Riverside)
This talk is organized as follows: 1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates. 2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations. 3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments. 4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.
Time permitting, (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity. (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors. (iii) Problems.
11/18/2020
Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)
Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.
11/19/2020
Eduardo Fradkin (University of Illinois at Urbana-Champaign)
Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.
Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.
Abstract: I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.
Abstract: Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics. I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter. How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!) remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
Abstract: The temperature versus doping phase diagram of the cuprate high-T_{c} superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa_{2}Cu_{3}O_{y }[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr_{2}CuO_{2}Cl_{2 }[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon. [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa_{2}Cu_{3}O_{y},” Nature Phys. 13, 250 (2017).
[2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr_{2}CuO_{2}Cl_{2},” Preprint at https://arxiv.org/abs/2008.06516 .
Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.
Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
The CMSA will host a weekly seminar running through 2020-21, where researchers from all areas of computer science present modern frontiers in computer science to the general mathematical audience. Talks shall be accessible to anyone with a good mathematical background; no domain-specific background is required. The seminar will run weekly on Tuesday 11:30 am ET.
Abstract: Living matter relies on the self organization of its components into higher order structures, on the molecular as well as on the cellular, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.
Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.
Previous Quantum Matter/Condensed Matter Seminar schedule information and video links can be found here.
As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place Wednesdays from 10:30 – 12:00pm on Zoom. The Condensed Matter/Math Seminar will take place on Thursdays from 10:30 – 12:00pm on Zoom. In addition to the Quantum Matter seminar, the CMSA will also be hosting a related seminar series on a Strongly Correlated Quantum Materials and High-Temperature Superconductors. Please email the seminar organizer to obtain a link.
The schedules for both seminars will be updated below as speakers are confirmed:
Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.
Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.
Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.
Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry. Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.
Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.
Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.
Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.
Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the `side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field. This work is based on arxiv: 2201.11681
Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv 2201.00903.
Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.
Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.
Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).
Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information- theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem. The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories. Our techniques generalize to other RG flow equations beyond Polchinski’s.
Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.
4/7/2022
Jung Hoon Han (Sungkyunkwan University, Suwon, South Korea)
Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.
References: [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021) [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022) [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation. [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.
Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)
4/20/2022 11:30–1:00 pm ET
Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)
Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.
Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.
Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.
Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.
Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.
Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045
Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+ → 3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.
Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.
Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.
Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory. Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.
Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.
[1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021) [2] V. Crepel and L. Fu, arXiv:2103.12060 [3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)
Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.
Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.
Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation. I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups. In particular, I expand on a subtlety first flagged by Greaves-Thomas.
Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.
Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.
Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.
Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion. For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.
Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.
Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases. We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006. Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples. After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.
Abstract: For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.
Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature. I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.
Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:
[1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155) [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL) [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)
Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.
Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).
Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.
Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems. Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]
Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.
Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.
Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.
Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators. References: [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015) [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017) [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017) [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)
7/28/2021
Max Metlitski (MIT)
Title: Boundary criticality of the O(N) model in d = 3 critically revisited.
Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry. Based on arXiv:2009.05119.
Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.
8/4/2021
Nathan Benjamin (Princeton & Caltech)
Title: Harmonic analysis of 2d CFT partition functions
Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.
8/5/2021
Hans-Werner Hammer (TU Darmstadt)
Title: Un-nuclear physics: conformal symmetry in nuclear reactions
Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.
8/11/2021
Piers Coleman (Rutgers)
Title: Order Fractionalization*
Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).
8/12/2012
Beni Yoshida (Perimeter Institute)
Title: On the firewall puzzle
Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.
8/18/2021
Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)
Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
8/19/2021
Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)
Title: “Probing the Standard Model of Particle Physics Using the Muon Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
8/25/2021
Hitoshi Murayama (UC Berkely & IPMU)
Title: Some Exact Results in QCD-like and Chiral Gauge Theories
Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.
Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”
I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.
Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.
Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.
2/3/2020
Philip Phillips (University of Illinois Urbana-Champaign)
Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates. [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).
Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).
Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
[1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789 [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523
Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.
Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.
Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.
Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics. I will start with the conceptual origin of this model as requested by the organizer. Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds. In the end, I will mention lattice models that generalize the Haah codes in two directions: general three manifolds and more than two qubits per site.
If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum. New lattice models in fracton physics raise an interesting question: what kinds of quantum field theories are they approximating if their continuous limits exist? Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.
Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as well as a series of seven heterotic strings, all of which are obtained by imposing unconventional GSO projections. Besides these classic examples, relatively little is known about the full space of non-SUSY theories. One of the reasons why non-SUSY strings have remained understudied is the fact that nearly all of them have closed string tachyons, and hence do not admit ten-dimensional flat space as a stable vacuum. The goal of this talk is two-fold. First, using recent advances in condensed matter theory, we will reinterpret GSO projections in terms of topological phases of matter, thereby providing a framework for the classification of non-SUSY strings. Having done so, we will show that for all non-SUSY theories in which a tachyon exists, it can be condensed to give a (meta)stable lower-dimensional vacuum. In many cases, these stable vacua will be two-dimensional string theories already known in the literature.
Abstract: We introduce the concepts of a symmetry-protected sign problem and symmetry-protected magic, defined by the inability of symmetric finite-depth quantum circuits to transform a state into a nonnegative real wave function and a stabilizer state, respectively. We show that certain symmetry protected topological (SPT) phases have these properties, as a result of their anomalous symmetry action at a boundary. For example, one-dimensional Z2 × Z2 SPT states (e.g. cluster state) have a symmetry-protected sign problem, and two-dimensional Z2 SPT states (e.g. Levin-Gu state) have both a symmetry-protected sign problem and magic. We also comment on the relation of a symmetry-protected sign problem to the computational wire property of one-dimensional SPT states and the greater implications of our results for measurement based quantum computing.
Abstract: ‘t Hooft anomalies provide a unique handle to study the nonperturbative infrared dynamics of strongly-coupled theories. Recently, it has been realized that higher-form global symmetries can also become anomalous, leading to further constraints on the infrared dynamics. In this talk, I show how one can turn on ‘t Hooft twists in the color, flavor, and baryon number directions in vector-like asymptotically-free gauge theories, which can be used to find new generalized ‘t Hooft anomalies. I give examples of the constraints the generalized anomalies impose on strongly-coupled gauge theories. Then, I argue that the anomaly inflow can explain a non-trivial intertwining that takes place between the light and heavy degrees of freedom on axion domain walls, which leads to the deconfinement of quarks on the walls. This phenomenon can be explicitly seen in a weakly-coupled model of QCD compactified on a small circle.
Abstract: Fracton phases show exotic properties, such as sub-extensive entropy, local particle-like excitation with restricted mobility, and so on. In order to find natural fermionic fracton phases, we explore supersymmetric quantum field theory with exotic symmetry. We use superfield formalism and write down the action of a supersymmetric version of one of the simplest models with exotic symmetry, the φ theory in 3+1 dimensions. It contains a large number of ground states due to the fermionic higher pole subsystem symmetry. Its residual entropy is proportional to the area instead of the volume. This theory has a self-duality similar to that of the φ theory. We also write down the action of a supersymmetric version of a tensor gauge theory, and discuss BPS fractons.
Abstract: Quantum systems out of equilibrium can exhibit different dynamical phases that are fundamentally characterized by their entanglement dynamics and entanglement scaling. Random quantum circuits with non-unitarity induced by measurement or other sources provide a large class of systems for us to investigate the nature of these different entanglement phases and associated criticality. While numerical studies have provided a lot of insight into the behavior of such quantum circuit models, analytical understanding of the entanglement criticality in these models has remained challenging in many cases. In this talk, I will focus on the random non-unitary fermionic Gaussian circuits, namely non-unitary circuits for non-interacting fermions. I will first present a numerical study of an entanglement critical phase in this type of circuit. Then, I will discuss the analytical understanding of general entanglement phases in this type of circuit via a general correspondence among (1) non-unitary fermionic Gaussian circuits, (2) fermionic Gaussian tensor network, and (3) unitary non-interacting fermions subject to quenched disorder. In particular, we show that the critical entanglement phase numerically found in the non-unitary Gaussian circuit without any symmetry can be described by the theory of (unitary) disordered metal in the symmetry class DIII. I will comment on the entanglement critical phases that correspond to unitary disordered fermion critical points or unitary disordered metals in other symmetry classes.
Abstract: Two-dimensional QCD models form an interesting playground for studying phenomena such as confinement and screening. In this talk I will describe one such model, namely a 2d SU(N) gauge theory with an adjoint and a fundamental fermion, and explain how to compute the spectrum of bound states using discretized light-cone quantization at large N. Surprisingly, the spectrum of the discretized theory exhibits a large number of exact degeneracies, for which I will provide two different explanations. I will also discuss how these degeneracies provide a physical picture of screening in 2d QCD with just a massless adjoint fermion. This talk is based on joint work with R. Dempsey and I. Klebanov.
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint
Abstract: Standard lore suggests that four-dimensional SU(N) gauge theory with 2 massless adjoint Weyl fermions (“adjoint QCD”) flows to a phase with confinement and chiral symmetry breaking. In this two-part talk, we will test and present new evidence for this lore. Our strategy involves realizing adjoint QCD in the deep IR of an RG flow descending from SU(N) Seiberg-Witten theory, deformed by a soft supersymmetry (SUSY) breaking mass for its adjoint scalars. We review what is known about the simplest case N=2, before presenting results for higher values of N. A crucial role in the analysis is played by a dual Lagrangian that originates from the multi-monopole points of Seiberg-Witten theory, and which can be used to explore the phase diagram as a function of the SUSY-breaking mass. The semi-classical phases of this dual Lagrangian suggest that the softly broken SU(N) theory traverses a sequence of phases, separated by first-order transitions, that interpolate between the Coulomb phase of Seiberg-Witten theory and the confining, chiral symmetry breaking phase expected for adjoint QCD.
Abstract: String-net models are exactly solvable lattice models that can realize a large class of (2+1)D topological phases. I will review basic aspects of these models, including their Hamiltonians, ground-state wave functions, and anyon excitations. I will also discuss the relationship between the original string-net models, proposed in 2004, and the more recent, “generalized’’, string-net models.
Abstract: The magnetoroton is the neutral excitation of a gapped fractional quantum Hall state. We argue that at zero momentum the magnetoroton has spin ±2, and show how the spin of the magnetoroton can be determined by polarized Raman scattering. We suggest that polarized Raman scattering may help to determine the nature of the ν=5/2 state. Ref: D.X. Nguyen and D.T. Son, arXiv:2101.02213.
Abstract: Since the discovery of high temperature superconductors in cuprates in 1986, many theoretical ideas have been proposed which have enriched condensed matter theory. Especially, the resonating valence bond (RVB) state for (doped) spin liquids is one of the most fruitful idea. In this talk, I would like to describe the development of RVB idea to broader class of materials, especially more conventional magnets. It is related to the noncollinear spin structures with spin chirality and associated quantal Berry phase applied to many phenomena and spintronics applications. It includes the (quantum) anomalous Hall effect, spin Hall effect, topological insulator, multiferroics, various topological spin textures, e.g., skyrmions, and nonlinear optics. I will show that even though the phenomena are extensive, the basic idea is rather simple and common in all of these topics.
Abstract: In this talk I will give an overview of recent developments in geometric constructions of field theory in string/M-theory and identifying higher form symmetries. The main focus will be on d>= 4 constructed from string/M-theory. I will also discuss realization in terms of holographic models in string theory. In the talk next week Lakshya Bhardwaj will speak about 1-form symmetries in class S, N=1 deformations thereof and the relation to confinement.
Title: Chiral edge modes, thermoelectric transport, and the Third Law of Thermodynamics Abstract: In this talk I will discuss several issues related to thermoelectric transport, with application to topological invariants of chiral topological phases in two dimensions. In the first part of the talk, I will argue in several different ways that the only topological invariants associated with anomalous edge transport are the Hall conductance and the thermal Hall conductance. Thermoelectric coefficients are shown to vanish at zero temperature and do not give rise to topological invariants. In the second part of the talk I will describe microscopic formulas for transport coefficients (Kubo formulas) which are valid for arbitrary interacting lattice systems. I will show that in general “textbook” Kubo formulas require corrections. This is true even for some dissipative transport coefficients, such as Seebeck and Peltier coefficients. I will also make a few remarks about “matching” (in the sense of Effective Field Theory) between microscopic descriptions of transport and hydrodynamics.
Abstract: We will discuss confinement in 4d N=1 theories obtained from 4d N=2 Class S theories after turning on supersymmetry breaking deformations. Confinement is characterised by the subgroup of the 1-form symmetry group of the theory that is left unbroken in a massive vacuum of the theory. We will see that the 1-form symmetry group is encoded in the Gaiotto curve associated to the Class S theory, and its spontaneous breaking in a vacuum is encoded in the N=1 curve (which plays the role of Seiberg-Witten curve for N=1) associated to that vacuum. Using this proposal, we will recover the expected properties of confinement in pure N=1 Yang-Mills theory and N=1 Yang-Mills theory with an adjoint chiral multiplet and generic superpotential. We will also be able to study the dependence of confinement on the choice of global form of gauge group and discrete theta parameters.
Abstract: QCD, the theory of the strong interactions, involves quarks interacting with non-Abelian gluon fields. This theory has many features that are difficult to impossible to see in conventional diagrammatic perturbation theory. This includes quark confinement, mass generation, and chiral symmetry breaking. This talk will be an elementary overview of the present framework for understanding how these effects come about.
TitleNon-abelian bosonization in two and three spatial dimensions and some applications Abstract: In this talk, we generalize Witten’s non-abelian bosonization in $(1+1)$-D to two and three spatial dimensions. Our theory applies to fermions with relativistic dispersion. The bosonized theories are non-linear sigma models with level-1 Wess-Zumino-Witten terms. As applications, we apply the bosonization results to the $SU(2)$ gauge theory of the $\pi$ flux mean-field theory of half-filled Hubbard model, critical spin liquids of “bipartite-Mott insulators” in 1,2,3 spatial dimensions, and twisted bilayer graphene.
Abstract: I will use Walker-Wang models to demonstrate the connection between 1-form symmetry-protected topological phases and topological measurement-based quantum computation. I will describe the classification of these phases in terms of symmetry domain walls and how these lead to “anomalous” 1-form symmetry actions on the boundary. I will also demonstrate that when the symmetries are strictly enforced these phases persist to finite temperatures and use this to explain symmetry-protected self-correction properties of the boundary topological phases.
Abstract: We know that different systems with the same unbroken global symmetry can nevertheless be in distinct phases of matter. These different “symmetry-protected topological” phases are characterized by protected (gapless) surface states. After reviewing this physics in interacting systems with global symmetries, I will describe how a different class of symmetries known as subsystem symmetries, which are neither local nor global, can also lead to protected gapless boundaries. I will discuss how some of these subsystem-symmetry protected phases are related (though not equivalent) to interacting higher-order topological insulators, with protected gapless modes along corners or hinges in higher dimensional systems.
Abstract: Diffeomorphisms and supersymmetry transformations act on all local quantum field theory operators, including on the Noether currents associated with other continuous symmetries, such as flavor or R-symmetry. I will discuss how quantum anomalies in these symmetries produce the local Bardeen-Zumino terms that ensure that the corresponding consistent Noether currents in the diffeomorphism and supersymmetry Ward identities are replaced by their covariant form. An important difference between diffeomorphisms and supersymmetry is that, while the effective action remains invariant under diffeomorphisms in the absence of a gravitational anomaly, the local terms in the supersymmetry Ward identity generated by quantum anomalies in other symmetries generally result in the non-invariance of the effective action under supersymmetry. In certain cases, however, supersymmetry invariance may be restored by suitably enlarging the multiplet that contains the anomalous Noether current. The structure of all local terms in the Ward identities due to quantum anomalies can be determined by solving the Wess-Zumino consistency conditions, which can be reformulated as a BRST cohomology problem. I will present a generalization of the standard BRST algebra for gauge theories and the associated anomaly descent procedure that is necessary for accommodating diffeomorphisms and supersymmetry transformations. I will also discuss how, in some cases, the solution of the Wess-Zumino consistency conditions in the presence of supersymmetry can be efficiently determined from a supersymmetric Chern-Simons action in one dimension higher through anomaly inflow. I will conclude with a brief discussion of the implications of the local terms in the supersymmetry Ward identity for the dependence of supersymmetric partition functions on backgrounds that admit Killing spinors.
5/6/2021
Weslei Bernardino Fontana (Boston University & Estadual)
Abstract: In this talk I will discuss how to obtain field theories for fracton lattice models. This is done by representing the lattice degrees of freedom with Dirac matrices, which are then related to continuum fields by means of a “bosonization” map. This procedure allows us to obtain effective theories which are of a Chern-Simons-like form. I will show that these Chern-Simons-like theories naturally encode the fractonic behavior of the excitations and that these theories can describe even type-II fracton phases.
Abstract: Many features of the cuprate phase diagram are a challenge for the usual tools of solid state physics. I will show how a perspective that takes into account both the localized and delocalized aspects of conduction electrons can explain, at least qualitatively, many of these features. More specifically, I will show that the work of several groups using cluster extensions of dynamical mean-field theory sheds light on the pseudogap, on the quantum-critical point and on d-wave superconductivity. I will argue that the charge transfer gap and oxygen hole content are the best indicators of strong superconductivity and that many observations are a signature of the influence of Mott physics away from half-filling. I will also briefly comment on what information theoretic measures tell us about this problem.
Abstract: I am going to argue that the non-vanishing gravitational anomaly in 2D CFT obstructs the existence of the well-defined notion of entanglement. As a corollary, we will also see that the non-vanishing gravitational anomaly means the non-existence of the lattice regulator generalising the Nielsen-Ninomiya theorem. Time permitting, I will also comment about the variation to other anomalies and/or to 6D and 4D. Finally, I will conclude the talk with possible future directions, in particular the implication it might have for the island conjecture. The talk is based on my recent paper with Simeon Hellerman and Domenico Orlando [2101.03320].
Abstract: The continuum formal path integral over Euclidean fermions in the background of a Euclidean gauge field is replaced by the quantum mechanics of an auxiliary system of non-self-interacting fermions. No-go “theorems” are avoided. The main features of chiral fermions arrived at by formal continuum arguments are preserved on the lattice.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Numerous experiments have explored the phases of the cuprates with increasing doping density p from the antiferromagnetic insulator. There is now strong evidence that the small p region is a novel phase of matter, often called the pseudogap metal, separated from conventional Fermi liquid at larger p by a quantum phase transition. Symmetry-breaking orders play a spectator role, at best, at this quantum phase transition. I will describe trial wavefunctions across this metal-metal transition employing hidden layers of ancilla qubits (proposed by Ya-Hui Zhang). Quantum fluctuations are described by a gauge theory of ghost fermions that carry neither spin nor charge. I will also describe a separate approach to this transition in a t-J model with random exchange interactions in the limit of large dimensions. This approach leads to a partly solvable SYK-like critical theory of holons and spinons, and a linear in temperature resistivity from time reparameterization fluctuations. Near criticality, both approaches have in common emergent fractionalized excitations, and a significantly larger entropy than naively expected.
Abstract: We study gapped boundaries characterized by “fermionic condensates” in 2+1 d topological order. Mathematically, each of these condensates can be described by a super commutative Frobenius algebra. We systematically obtain the species of excitations at the gapped boundary/ junctions, and study their endomorphisms (ability to trap a Majorana fermion) and fusion rules, and generalized the defect Verlinde formula to a twisted version. We illustrate these results with explicit examples. We will also comment on the connection with topological defects in spin CFTs. We will review necessary mathematical details of Frobenius algebra and their modules that we made heavy use of.
Abstract: We revisit ‘t Hooft anomalies in (1+1)d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1)d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-unitary or non-compact theories; on the other hand, without insisting on unitarity, the exotic anomalies present a small caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) x SO(2) classical Chern-Simons action, with a boundary condition that matches the SO(2) gauge field with the (1+1)d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The holomorphic bc ghost system realizes all the exotic consistent anomalies.
Abstract: Certain patterns of symmetry fractionalization in (2+1)D topologically ordered phases of matter can be anomalous, which means that they possess an obstruction to being realized in purely (2+1)D. In this talk, I will explain our recent results showing how to compute the anomaly for symmetry-enriched topological (SET) states of bosons in complete generality. Given any unitary modular tensor category (UMTC) and symmetry fractionalization class for a global symmetry group G, I will show how to define a (3+1)D topologically invariant path integral in terms of a state sum for a G symmetry- protected topological (SPT) state. This also determines an exactly solvable Hamiltonian for the system which possesses a (2+1)D G symmetric surface termination that hosts deconfined anyon excitations described by the given UMTC and symmetry fractionalization class. This approach applies to general symmetry groups, including anyon-permuting and anti-unitary symmetries. In the case of unitary orientation-preserving symmetries, our results can also be viewed as providing a method to compute the H4(G,U(1)) obstruction that arises in the theory of G-crossed braided tensor categories, for which no general method has been presented to date. This is joint work with D. Bulmash, presented in arXiv:2003.11553
Abstract: I’ll review the basic construction of Randall-Sundrum braneworlds and some of their applications to formal problems in quantum field theory. I will highlight some recent results regarding scenarios with mismatched brane tensions. In the last part of the talk, I’ll review how RS branes have led to exciting new results regarding evaporation of black holes and will put emphasis on the interesting role the graviton mass plays in these discussions.
Abstract: Quantum entanglement has played a key role in studying emergent phenomena in strongly-correlated many-body systems. Remarkably, The entanglement properties of the ground state encodes information on the nature of excitations. Here we introduce two new entanglement measures $g(A:B)$ and $h(A:B)$ which characterizes certain tripartite entanglement between $A$, $B$, and the environment. The measures are based off of the entanglement of purification and the reflected entropy popular among holography. For 1D states, the two measures are UV insensitive and yield universal quantities for symmetry-broken, symmetry preserved, and critical phases. We conclude with a few remarks regarding applications to 2D phases.
Abstract: In this second talk, I will focus on (nearly) solvable models of metal-metal transition in random systems. The t-J model with random and all-to-all hopping and exchange can be mapped onto a quantum impurity model coupled self-consistently to an environment (the mapping also applies to a t-J model in a large dimension lattice, with random nearest-neighbor exchange). Such models will be argued to exhibit metal-metal quantum phase transitions in the universality class of the SYK model, accompanied by a linear-in-T resistivity from time reparameterization fluctuations. I will also present the results of exact diagonalization of random t-J clusters, obtained recently with Henry Shackleton, Alexander Wietek, and Antoine Georges.
Abstract: The cuprate superconductors exhibit the highest ambient-pressure superconducting transition temperatures (T c ), and after more than three decades of extraordinary research activity, continue to pose formidable scientific challenges. A major experimental obstacle has been to distinguish universal phenomena from materials- or technique-dependent ones. Angle-resolved photoemission spectroscopy (ARPES) measures momentum-dependent single-particle electronic excitations and has been invaluable in the endeavor to determine the anisotropic momentum-space properties of the cuprates. HgBa 2 CuO 4+d (Hg1201) is a single-layer cuprate with a particularly high optimal T c and a simple crystal structure; yet there exists little information from ARPES about the electronic properties of this model system. I will present recent ARPES studies of doping-, temperature-, and momentum-dependent systematics of near-nodal dispersion anomalies in Hg1201. The data reveal a hierarchy of three distinct energy scales which establish several universal phenomena, both in terms of connecting multiple experimental techniques for a single material, and in terms of connecting comparable spectral features in multiple structurally similar cuprates.
Abstract: We discover a wide range of new nonperturbative effects in quantum gravity, namely moduli spaces of constrained instantons of the Einstein-Hilbert action. We find these instantons in all spacetime dimensions, for AdS and dS. Many can be written in closed form and are quadratically stable. In 3D AdS, where the full gravitational path integral is more tractable, we study constrained instantons corresponding to Euclidean wormholes. We show that they encode the energy level statistics of microstates of BTZ black holes, which precisely agrees with a quantitative prediction from random matrix theory.
Abstract: The infamous sign problem leads to an exponential complexity in Monte Carlo simulations of generic many-body quantum systems. Nevertheless, many phases of matter are known to admit a sign-problem-free representative, allowing efficient simulations on classical computers. Motivated by long standing open problems in many-body physics, as well as fundamental questions in quantum complexity, the possibility of intrinsic sign problems, where a phase of matter admits no sign-problem-free representative, was recently raised but remains largely unexplored. I will describe results establishing the existence of intrinsic sign problems in a broad class of topologically ordered phases in 2+1 dimensions. Within this class, these results exclude the possibility of ‘stoquastic’ Hamiltonians for bosons, and of sign-problem-free determinantal Monte Carlo algorithms for fermions. The talk is based on arxiv:2005.05566 and 2005.05343.
Abstract: In this talk, I will describe how symmetry can enrich strong-randomness quantum critical points and phases, and lead to robust topological edge modes coexisting with critical bulk fluctuations. Our approach provides a systematic construction of strongly disordered gapless topological phases. Using real space renormalization group techniques, I will discuss the boundary and bulk critical behavior of symmetry-enriched random quantum spin chains, and argue that nonlocal observables and boundary critical behavior are controlled by new renormalization group fixed points. I will also discuss the interplay between disorder, quantum criticality and topology in higher dimensions using disordered gauge theories.
Abstract: Orbifolds are ubiquitous in physics, not just explicitly in CFT, but going undercover with names like Kramers-Wannier duality, Jordan-Wigner transformation, or GSO projection. All of these names describe ways to “topologically manipulate” a theory, transforming it to a new one, but leaving the local dynamics unchanged. In my talk, I will answer the question: given some (1+1)d QFT, how many new theories can we produce by topological manipulations? To do so, I will outline the relationship between these manipulations and (2+1)d Dijkgraaf-Witten TFTs, and illustrate both the conceptual and computational power of the relationship. Ideas from high-energy, condensed-matter, and pure math will show up in one form or another. Based on work with Davide Gaiotto [arxiv:2008.05960].
Abstract: Conformal bootstrap is a powerful method to study conformal field theory (CFT) in arbitrary spacetime dimensions. Sometimes interesting CFTs such as O(N) Wilson-Fisher (WF) CFTs sit at kinks of numerical bootstrap bounds. In this talk I will first give a brief introduction to conformal bootstrap, and then discuss a new family of kinks (dubbed non-WF kinks) of numerical bootstrap bounds of O(N) symmetric CFTs. The nature of these new kinks remains mysterious, but we manage to understand few special cases, which already hint interesting physics. In 2D, the O(4) non-WF kink turns out to be the familiar SU(2)_1 Wess-Zumino-Witten model. We further consider its dimensional continuation towards the 3D SO(5) deconfined phase transition, and we find the kink disappears at fractional dimension (around D=2.7), suggesting the 3D SO(5) deconfined phase transition is pseudo-critical. At last, based on the analytical solution at infinite N limit we speculate that there exists a new family of O(N) (or SO(N)) true CFTs for N large enough, which might be a large-N generalization of SO(5) DQCP.
Abstract: The pseudogap phase of cuprate superconductors is arguably the most enigmatic phase of quantum matter. We aim to shed new light on this phase by investigating the non- superconducting ground state of several cuprate materials at low temperature across a wide doping range, suppressing superconductivity with a magnetic field. Hall effect measurements across the pseudogap critical doping p* reveal a sharp drop in carrier density n from n = 1 + p above p* to n = p below p, signaling a major transformation of the Fermi surface. Angle-dependent magneto-resistance (ADMR) directly reveals a change in Fermi surface topology across p. From specific heat measurements, we observe the classic thermodynamic signatures of quantum criticality: the electronic specific heat C el shows a sharp peak at p, where it varies in temperature as C el ~ – T logT. At p and just above, the electrical resistivity is linear in T at low T, with an inelastic scattering rate that obeys the Planckian limit. Finally, the pseudogap phase is found to have a large negative thermal Hall conductivity, which extends to zero doping. We show that the pseudogap phase makes phonons become chiral. Understanding the mechanisms responsible for these various new signatures will help elucidate the nature of the pseudogap phase.
10/21/2020
Oleg Dubinkin (University of Illinois at Urbana–Champaign)
Abstract: The most basic characteristic of an electrically insulating system is the absence of charged currents. This property alone guarantees the conservation of the overall dipole moment (i.e., the first multipole moment) in the low-energy sector. It is then natural to inquire about the fate of the transport properties of higher electric multipole moments, such as the quadrupole and octupole moments, and ask what properties of the insulating system can guarantee their conservation. In this talk I will present a suitable refinement of the notion of an insulator by investigating a class of systems that conserve both the total charge and the total dipole moment. In particular, I will consider microscopic models for systems that conserve dipole moments exactly and show that one can divide charge insulators into two new classes: (i) a dipole metal, which is a charge-insulating system that supports dipole-moment currents, or (ii) a dipole insulator which is a charge-insulating system that does not allow dipole currents and thus, conserves an overall quadrupole moment. In the second part of my talk I will discuss a more mathematical description of dipole-conserving systems where I show that a conservation of the overall dipole moment can be naturally attributed to a global 1-form electric U(1) symmetry, which is in direct analogy to how the electric charge conservation is guaranteed by the global U(1) phase-rotation symmetry for electrically charged particles. Finally, this new approach will allow me to construct a topological response action which is especially useful for characterizing Higher-Order Topological phases carrying quantized quadrupole moments.
Abstract: I will give an overview of my work with Aasen and Mong on using fusion categories to find and analyse topological defects in two-dimensional classical lattice models and quantum chains. These defects possess a variety of remarkable properties. Not only is the partition function independent of deformations of their path, but they can branch and fuse in a topologically invariant fashion. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-symmetry-related ground states as well as in the low-energy spectrum. The universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. I also will describe how terminating defect lines allows the construction of fractional-spin conserved currents, giving a linear method for Baxterization, I.e. constructing integrable models from a braided tensor category.
Abstract: The underdoped Cuprate exhibits a rich variety of unusual properties that have been exposed after years of experimental investigations. They include a pseudo-gap near the anti-nodal points and “Fermi arcs” of gapless excitations, together with a variety of order such as charge order, nematicity and possibly loop currents and time reversal and inversion breaking. I shall argue that by making a single assumption of strong pair fluctuations at finite momentum (Pair density wave), a unified description of this phenomenology is possible. As an example, I will focus on a description of the ground state that emerges when superconductivity is suppressed by a magnetic field which supports small electron pockets. [Dai, Senthil, Lee, Phys Rev B101, 064502 (2020)] There is some support for the pair density wave hypothesis from STM data that found charge order at double the usual wave-vector in the vicinity of vortices, as well as evidence for a fragile form of superconductivity persisting to fields much above Hc2. I shall suggest a more direct experimental probe of the proposed fluctuating pair density wave.
Abstract: The twisted bilayer graphene (TBG) near the magic angle around 1 degree hosts topological flat moiré electron bands, and exhibits a rich tunable strongly interacting physics. Correlated insulators and Chern insulators have been observed at integer fillings nu=0,+-1,+-2,+-3 (number of electrons per moiré unit cell). I will first talk about the enhanced U(4) or U(4)xU(4) symmetries of the projected TBG Hamiltonian with Coulomb interaction in various combinations of the flat band limit and two chiral limits. The symmetries in the first chiral and/or flat limits allow us to identify exact or approximate ground/low-energy (Chern) insulator states at all the integer fillings nu under a weak assumption, and to exactly compute charge +-1, +-2 and neutral excitations. In the realistic case away from the first chiral and flat band limits, we find perturbatively that the ground state at integer fillings nu has Chern number +-mod(nu,2), which is intervalley coherent if nu=0,+-1,+-2, and is valley polarized if nu=+-3. We further show that at nu=+-1 and +-2, a first order phase transition to a Chern number 4-|nu| state occurs in an out-of-plane magnetic field. Our calculation of excitations also rules out the Cooper pairing at integer fillings nu from Coulomb interaction in the flat band limit, suggesting other superconductivity mechanisms. These analytical results at nonzero fillings are further verified by a full Hilbert space exact diagonalization (ED) calculation. Furthermore, our ED calculation for nu=-3 implies a phase transition to possible translationally breaking or metallic phases at large deviation from the first chiral limit.
Abstract: The analysis of complex systems often hinges on our ability to extract the relevant degrees of freedom from among the many others. Recently the information bottleneck (IB), a signal processing tool, was proposed as an unbiased means for such order parameter extraction. While IB optimization was considered intractable for many years, new deep-learning-based techniques seem to solve it quite efficiently. In this talk, I’ll introduce IB in the real-space renormalization context (a.k.a. RSMI), along with two recent theoretical results. One links IB optimization to the short-rangeness of coarse-grained Hamiltonians. The other provides a dictionary between the quantities extracted in IB, understood only qualitatively thus far, and relevant operators in the underlying field theory (or eigenvectors of the transfer matrix). Apart from relating field-theory and information, these results suggest that deep learning in conjunction with IB can provide useful and interpretable tools for studying complex systems.
Abstract: High‐temperature superconductivity in cupper oxides, with critical temperature well above what wasanticipated by the BCS theory, remains a major unsolved physics problem. The problem is fascinating because it is simultaneously simple ‐ being a single band and 1⁄2 spin system, yet extremely rich ‐ boasting d‐wave superconductivity, pseudogap, spin and charge orders, and strange metal phenomenology. For this reason, cuprates emerge as the most important model system for correlated electrons – stimulating conversations on the physics of Hubbard model, quantum critical point, Planckian metal and beyond. Central to this debate is whether the Hubbard model, which is the natural starting point for the undoped magnetic insulator, contains the essential ingredients for key physics in cuprates. In this talk, I will discuss our photoemission evidence for a multifaceted answer to this question [1‐3]. First, we show results that naturally points to the importance of Coulomb and magnetic interactions, including d‐wave superconducting gap structure [4], exchange energy (J) control of bandwidth in single‐hole dynamics [5]. Second, we evidence effects beyond the Hubbard model, including band dispersion anomalies at known phonon frequencies [6, 7], polaronic spectral lineshape and the emergence of quasiparticle with doping [8]. Third, we show properties likely of hybrid electronic and phononic origin, including the pseudogap [9‐11], and the almost vertical phase boundary near the critical 19% doping [12]. Fourth, we show examples of small q phononic coupling that cooperates with d‐wave superconductivity [13‐15]. Finally, we discuss recent experimental advance in synthesizing and investigating doped one‐dimensional (1D) cuprates [16]. As theoretical calculations of the 1D Hubbard model are reliable, a robust comparison can be carried out. The experiment reveals a near‐neighbor attractive interaction that is an order of magnitude larger than the attraction generated by spin‐superexchange in the Hubbard model. Addition of such an attractive term, likely of phononic origin, into the Hubbard model with canonical parameters provides a quantitative explanation for all important experimental observable: spinon and holon dispersions, and holon‐ holon attraction. Given the structural similarity of the materials, It is likely that an extended two‐dimensional (2D) Hubbard model with such an attractive term, will connect the dots of the above four classes of experimental observables and provide a holistic understanding of cuprates, including the elusive d‐wave superconductivity in 2D Hubbard model.
[1] A. Damascelli, Z. Hussain, and Z.‐X. Shen, Review of Modern Physics, 75, 473 (2003) [2] M. Hashimoto et al., Nature Physics 10, 483 (2014) [3] JA Sobota, Y He, ZX Shen ‐ arXiv preprint arXiv:2008.02378, 2020; submitted to Rev. of Mod. Phys. [4] Z.‐X. Shen et al., Phys. Rev. Lett. 70, 1553 (1993) [5] B.O. Wells et al., Phys. Rev. Lett. 74, 964 (1995) [6] A. Lanzara et al., Nature 412, 510 (2001) [7] T. Cuk et al., Phys. Rev. Lett., 93, 117003 (2004) [8] K.M. Shen et al., Phys. Rev. Lett., 93, 267002 (2004) [9] D.M. King et al., J. of Phys. & Chem of Solids 56, 1865 (1995) [10] D.S. Marshall et al., Phy. Rev. Lett. 76, 484 (1996) [11] A.G. Loeser et al., Science 273, 325 (1996) [12] S. Chen et al., Science, 366, 6469 (2019) [13] T.P. Devereaux, T. Cuk, Z.X. Shen, N. Nagaosa, Phys. Rev. Lett., 93, 117004 (2004) [14] S. Johnston et al., Phys. Rev. Lett. 108, 166404 (2012) [15] Yu He et al., Science, 362, 62 (Oct. 2018) [16] Z. Chen, Y. Wang et al., preprint, 2020
Abstract: Symmetry protected topological (SPT) phases are inevitable phases of quantum matter that are distinct from trivial phases only in the presence of unbroken global symmetries. These are characterized by anomalous boundaries which host emergent symmetries and protected degeneracies and gaplessness. I will present results from an ongoing series of works with Juven Wang on boundary symmetries of fermionic SPT phases, generalizing a previous work: arxiv:1804.11236. In 1+1 d, I will argue that the boundary of all intrinsically fermionic SPT phases can be recast as supersymmetric (SUSY) quantum mechanical systems and show that by extending the boundary symmetry to that of the bulk, all fermionic SPT phases can be unwound to the trivial phase. I will also present evidence that boundary SUSY seems to be present in various higher dimensional examples also and might even be a general feature of all intrinsically fermionic SPT phases.
11/12/2020
Chandra Varma (University of California, Riverside)
This talk is organized as follows: 1. Physical Principles leading to Loop-current order and quantum criticality as the central feature in the physics of Cuprates. 2. Summary of the essentially exact solution of the dissipative xy model for Loop-current fluctuations. 3. Quantitative comparison of theory for the quantum-criticality with a variety of experiments. 4. Topological decoration of loop-current order to understand ”Fermi-arcs” and small Fermi-surface magneto-oscillations.
Time permitting, (i) Quantitative theory and experiment for fluctuations leading to d-wave superconductivity. (ii) Extensions to understand AFM quantum-criticality in heavy-fermions and Fe-based superconductors. (iii) Problems.
11/18/2020
Antoine Georges (Collège de France, Paris and Flatiron Institute, New York)
Abstract: Simplified as it is, the Hubbard model embodies much of the complexity of the `strong correlation problem’ and has established itself as a paradigmatic model in the field. In this talk, I will argue that several key aspects of its physics in two dimensions can now be established beyond doubt, thanks to the development of controlled and accurate computational methods. These methods implement different and complementary points of view on the quantum many-body problem. Along with pushing forward each method, the community has recently embarked into a major effort to combine and critically compare these approaches, and in several instances a consistent picture of the physics has emerged as a result. I will review in this perspective our current understanding of the emergence of a pseudogap in both the weak and strong coupling regimes. I will present recent progress in understanding how the pseudogap phase may evolve into a stripe-dominated regime at low temperature, and briefly address the delicate question of the competition between stripes and superconductivity. I will also emphasize outstanding questions which are still open, such as the possibility of a Fermi surface reconstruction without symmetry breaking. Whenever possible, connections to the physics of cuprate superconductors will be made. If time permits, I may also address the question of Planckian transport and bad metallic transport at high temperature.
11/19/2020
Eduardo Fradkin (University of Illinois at Urbana-Champaign)
Abstract: I will argue that the orders that are present in high temperature superconductors naturally arise with the same strength and are better regarded as intertwined rather than competing. I illustrate this concept in the context of the orders that are present in the pair-density-wave state and the phase diagrams that result from this analysis.
Abstract: Strongly correlated electron systems often show bad-metal behavior, as operationally specified in terms of a resistivity at room temperature that reaches or exceeds the Mott-Ioffe-Regel limit. They display a rich landscape of electronic orders, which provide clues to the underlying microscopic physics. Iron-based superconductors present a striking case study, and have been the subject of extensive efforts during the past decade or so. They are well established to be bad metals, and their phase diagrams prominently feature various types of electronic orders that are essentially always accompanied by nematicity. In this talk, I will summarize these characteristic features and discuss our own efforts towards understanding the normal state through the lens of the electronic orders and their fluctuations. Implications for superconductivity will be briefly discussed. In the second part of the talk, I will consider the nematic correlations that have been observed in the graphene-based moiré narrow-band systems. I will present a theoretical study which demonstrates nematicity in a “fragile insulator”, predicts its persistence in the bad metal regime and provides an overall perspective on the phase diagram of these correlated systems.
Abstract: I discuss the interplay between non-Fermi liquid behaviour and pairing near a quantum-critical point (QCP) in a metal. These tendencies are intertwined in the sense that both originate from the same interaction mediated by gapless fluctuations of a critical order parameter. The two tendencies compete because fermionic incoherence destroys the Cooper logarithm, while the pairing eliminates scattering at low energies and restores fermionic coherence. I discuss this physics for a class of models with an effective dynamical interaction V (Ω) ~1/|Ω|^γ (the γ-model). This model describes, in particular, the pairing at a 2D Ising-nematic critical point in (γ=1/3), a 2D antiferromagnetic critical point (γ=1/2) and the pairing by an Einstein phonon with vanishing dressed Debye frequency (γ=2). I argue the pairing wins, unless the pairing component of the interaction is artificially reduced, but because of fermionic incoherence in the normal state, the system develops a pseudogap, preformed pairs behaviour in the temperature range between the onset of the pairing at Tp and the onset of phase coherence at the actual superconducting Tc. The ratio Tc/Tp decreases with γ and vanishes at γ =2. I present two complementary arguments of why this happens. One is the softening of longitudinal gap fluctuations, which become gapless at γ =2. Another is the emergence of a 1D array of dynamical vortices, whose number diverges at γ =2. I argue that once the number of vortices becomes infinite, quasiparticle energies effectively get quantized and do not get re-arranged in the presence of a small phase variation. I show that a new non-superconducting ground state emerges at γ >2.
Abstract: Ideas from the early1990s for regulating chiral fermions in lattice gauge theory led to a number of developments which paralleled roughly concurrent and independent discoveries in condensed matter physics. I show how the Integer Quantum Hall Effect, Chern Insulators, Topological Insulators, and Majorana edge states all play a role in lattice gauge theories, and how one can also find relativistic versions of the Fractional Quantum Hall Effect, the Quantum Spin Hall Effect and related exotic forms of matter. How to construct a nonperturbative regulator for chiral gauge theories (like the Standard Model!) remains an open challenge, however, one that may require new insights from condensed matter physics into exotic states of matter.
Abstract: The temperature versus doping phase diagram of the cuprate high-T_{c} superconductors features an enigmatic pseudogap region whose microscopic origin remains a subject of intensive study. Experimentally resolving its symmetry properties is imperative for narrowing down the list of possible explanations. In this talk I will give an overview of how optical second harmonic generation (SHG) can be used as a sensitive probe of symmetry breaking, and recap the ways it has been used to solve outstanding problems in condensed matter physics. I will then describe how we have been applying SHG polarimetry and spectroscopy to interrogate the cuprate pseudogap. In particular, I will discuss our data on YBa_{2}Cu_{3}O_{y }[1], which show an order parameter-like increase in SHG intensity below the pseudogap temperature T* across a broad range of doping levels. I will then focus on our more recent results on a model parent cuprate Sr_{2}CuO_{2}Cl_{2 }[2], where evidence of anomalous broken symmetries surprisingly also exists. Possible connections between these observations will be speculated upon. [1] L. Zhao, C. A. Belvin, R. Liang, D. A. Bonn, W. N. Hardy, N. P. Armitage and D. Hsieh, “A global inversion-symmetry-broken phase inside the pseudogap region of YBa_{2}Cu_{3}O_{y},” Nature Phys. 13, 250 (2017).
[2] A. de la Torre, K. L. Seyler, L. Zhao, S. Di Matteo, M. S. Scheurer, Y. Li, B. Yu, M. Greven, S. Sachdev, M. R. Norman and D. Hsieh. “Anomalous mirror symmetry breaking in a model insulating cuprate Sr_{2}CuO_{2}Cl_{2},” Preprint at https://arxiv.org/abs/2008.06516 .
Abstract: In this talk, I will introduce an analytic bootstrap approach for two-point correlation functions in CFTs on real projective space, and CFTs with a conformal boundary. We will use holography as a kinematical tool to derive universal results. By examining the conformal block decomposition properties of exchange diagrams in AdS space, we identify a useful new basis for decomposing correlators. The dual basis gives rise to a basis of functionals, whose actions we can compute explicitly via holography. Applying these functionals to the crossing equations, we can systematically extract constraints on the CFT data in the form of sum rules. I will demonstrate this analytic method in the canonical example of \phi^4 theory in d=4-\epsilon, fixing the CFT data to \epsilon^2.
Abstract: The complex phenomenon in the high-Tc cuprate calls for a microscopic understanding based on general principles. In this Lecture, an exact organizing principle for a typical doped Mott insulator will be presented, in which the fermion sign structure is drastically reduced to a mutual statistics. Its nature as a long-range spin-charge entanglement of many-body quantum mechanics will be exemplified by exact numerical calculations. The phase diagram of the cuprate may be unified in a “bottom-up” fashion by a “parent” ground state ansatz with hidden orders constructed based on the organizing principle. Here the pairing mechanism will go beyond the “RVB” picture and the superconducting state is of non-BCS nature with modified London equation and novel elementary excitations. In particular, the Bogoliubov/Landau quasiparticle excitation are emerging with a two-gap structure in the superconducting state and the Fermi arc in a pseudogap regime. A mathematic framework of fractionalization and duality transformation guided by the organizing principle will be introduced to describe the above emergent phenomenon.
Abstract: Despite the fact that papers submitted to glossy journals universally start by bemoaning the absence of theoretical understanding, I will argue that the answer to the title question is “quite a lot.” To focus the discussion, I will take the late P.W. Anderson’s “Last Words on the Cuprates” (arXiv:1612.03919) as a point of departure, although from a perspective that differs from his in many key points.
The CMSA will host a weekly seminar running through 2020-21, where researchers from all areas of computer science present modern frontiers in computer science to the general mathematical audience. Talks shall be accessible to anyone with a good mathematical background; no domain-specific background is required. The seminar will run weekly on Tuesday 11:30 am ET.
Abstract: Living matter relies on the self organization of its components into higher order structures, on the molecular as well as on the cellular, organ or even organism scale. Collective motion due to active transport processes has been shown to be a promising route for attributing fascinating order formation processes on these different length scales. Here I will present recent results on structure formation on actively transported actin filaments on lipid membranes and vesicles, as well as the cell migration induced structure formation in the developmental phase of mammary gland organoids. For both systems spherical structures with persistent collective rotations are observed.
Title: Exotic quantum matter: From lattice gauge theory to hyperbolic lattices
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.
During the 2021–22 academic year, the CMSA will be hosting a Member Seminar, organized by Therese YingYing Wu and Itamir Shamir in the Fall 2021 semester and Freid Tong and Gabriel Wong during Spring 2022. This seminar will take place on Fridays at 9:30am – 10:30am (Boston time). The meetings will take place virtually on Zoom. All CMSA postdocs/members are required to attend the weekly CMSA Members’ Seminars, as well as the weekly CMSA Colloquium series.
The schedule below will be updated as talks are confirmed.
Abstract: In this talk, I will start by reviewing central ideas of the so-called Swampland Program. The Swampland Program aims to identify criteria that distinguish low-energy effective field theories, that can be consistently coupled to quantum gravity, from those theories that become inconsistent in the presence of quantum gravity.
In my talk I will specialize to four-dimensional effective field theories with N=2 and N=1 supersymmetry. In weakly-coupled regions of the scalar field space of such theories, it has been shown that light strings are crucial to realize certain Swampland criteria. Complementary to that, the focus of this talk will be on the role of such light strings away from these weak-coupling regimes. In this context, I will first discuss a relation between light perturbative strings and strong coupling singularities in the Kähler moduli space of 4d N=1 compactifications of F-theory. More precisely, in regions of moduli space, in which a critical string classically becomes light, I will show that non-perturbative corrections yield to strong coupling singularities for D7-brane gauge theories which obstruct weak-coupling limits. Moreover, I will demonstrate that in the vicinity of this strong coupling singularity, the critical, light string in fact leaves the spectrum of BPS strings thereby providing an explanation for the obstruction of the weak coupling limit.
I will then move on and discuss the backreaction of perturbative strings in 4d EFTs. Away from the string core, the backreaction of such strings necessarily leads to strong coupling regions where naively the energy stored in the backreaction diverges. I will show how the introduction of additional non-critical strings can regulate this backreaction and how this can be used to study the spectrum of BPS strings and their tensions even beyond weak coupling regions. In this context, I will demonstrate how the requirement, that the total string tension should not exceed the Planck scale, constrains the possible BPS string charges.
Abstract: I will talk about Anti-de Sitter solutions in string theory with a parametric separation between the AdS curvature scale and the Kaluza-Klein scale. In particular, I will discuss recent progress on computing backreaction corrections in such solutions, and I will explain how to construct solutions without Romans mass that can be lifted to M-theory.
Abstract: We will consider a class of Calabi-Yau varieties given by cyclic branched covers of a fixed semi Fano manifold. The first prototype example goes back to Euler, Gauss and Legendre, who considered 2-fold covers of P1 branched over 4 points. Two-fold covers of P2 branched over 6 lines have been studied more recently by many authors, including Matsumoto, Sasaki, Yoshida and others, mainly from the viewpoint of their moduli spaces and their comparisons. I will outline a higher dimensional generalization from the viewpoint of mirror symmetry. We will introduce a new compactification of the moduli space cyclic covers, using the idea of ‘abelian gauge fixing’ and ‘fractional complete intersections’. This produces a moduli problem that is amenable to tools in toric geometry, particularly those that we have developed jointly in the mid-90’s with S. Hosono and S.-T. Yau in our study of toric Calabi-Yau complete intersections. In dimension 2, this construction gives rise to new and interesting identities of modular forms and mirror maps associated to certain K3 surfaces. We also present an essentially complete mirror theory in dimension 3, and discuss generalization to higher dimensions. The lecture is based on joint work with Shinobu Hosono, Tsung-Ju Lee, Hiromichi Takagi, Shing-Tung Yau.
Abstract: The Riemannian positive mass theorem states that a complete asymptotically flat manifold with nonnegative scalar curvature must have nonnegative ADM mass. This inequality comes with a rigidity statement that says that if the mass is zero, then the manifold must be Euclidean space. This naturally leads to the question of stability. In this talk, I will discuss various results related to this question.
Abstract: In this talk I will discuss about Amplituhedra – generalizations of polytopes inside the Grassmannian – recently introduced by physicists as new geometric constructions encoding interactions of elementary particles in certain Quantum Field Theories. In particular, I will explain how the problem of finding triangulations of Amplituhedra is connected to computing scattering amplitudes of N=4 super Yang-Mills theory. Triangulations of polygons are encoded in the associahedron studied by Stasheff in the sixties; in the case of polytopes, triangulations are captured by secondary polytopes constructed by Gelfand et al. in the nineties. Whereas a “secondary” geometry describing triangulations of Amplituhedra is still not known, and we pave the way for such studies. We will discuss how the combinatorics of triangulations interplays with T-duality from String Theory, in connection with a dual object we define – the Momentum Amplituhedron. A generalization of T-duality led us to discover a striking duality between triangulations of Amplituhedra of “m=2” type and the ones of a seemingly unrelated object – the Hypersimplex. The latter is a polytope which has been central in many contexts, such as matroid theory, torus orbits in the Grassmannian, and tropical geometry. Based on joint works with Lauren Williams, Melissa Sherman-Bennett, Tomasz Lukowski [arXiv:2104.08254, arXiv:2002.06164].
Abstract: This talk aims to provide a physics framework to understand quadratic reciprocity. Specifically, we consider a deformation of the two-dimensional free scalar field theory by raising the Laplacian to a positive real power. It turns out that the resulting non-local generalized free action is invariant under two commuting actions of the global conformal symmetry algebra, although it is no longer invariant under the full Witt algebra. The deformation is also closely related to dimensional regularization. Furthermore, there is an adelic version of this family of conformal field theories, parameterized by the choice of a number field, together with a Hecke character. Tate’s thesis gives the Green’s functions of these theories, and ensures that these Green’s functions satisfy an adelic product formula. In particular, the local L-factors contribute to the prefactors of these Green’s functions. Quadratic reciprocity turns out to be a consequence of an adelic version of a holomorphic factorization property of this family of theories on a quadratic extension of Q. At the Archimedean place, the desired holomorphic factorization follows from the global conformal symmetry.
Abstract: I’ll describe some recent work spanning a couple of different papers on the topics mentioned in the title: Positive Mass, Density, and Scalar Curvature on Noncompact Manifolds. Two of these are with R. Unger, Prof. S-T. Yau, and two others are with R. Unger, and Prof. D. A. Lee.
Abstract: SUSY curves are algebraic curves with additional supersymmetric or supergeometric structures. In this talk, I will present the construction of dual graphs of SUSY curves with Neveu–Schwarz and Ramond punctures. Then, I will introduce the concept of the metrized SUSY graph and the moduli space of the metric SUSY graphs. I will outline its geometric and topological properties, followed by a discussion on the connection with the classical case.
Abstract: A GKZ system, introduced by Gelfand, Kapranov, and Zelevinsky, is a system of partial differential equations generalizing the hypergeometric structure studied by Euler and Gauss. The solutions to GKZ systems have been found applications in various branches of mathematics including number theory, algebraic geometry and mirror symmetry. In this talk, I will explain the details and demonstrate how to find the Riemann–Hilbert partner of the GKZ system with a fractional parameter which arises from the B model of singular CY varieties. This is a joint work with Dingxin Zhang.
Abstract: In this talk, we develop a minimal model of morphogenesis of a surface where the dynamics of the intrinsic geometry is diffusive growth sourced by topological defects. We show that a positive (negative) defect can dynamically generate a cone (hyperbolic cone). We analytically explain features of the growth profile as a function of position and time, and predict that in the presence of a positive defect, a bump forms with height profile h(t) ~ t^(1/2) for early times t. To incorporate the effect of the mean curvature, we exploit the fact that for axisymmetric surfaces, the extrinsic geometry can be deduced entirely by the intrinsic geometry. We find that the resulting stationary geometry, for polar order and small bending modulus, is a deformed football. We apply our framework to various biological systems. In an ex-vivo setting of cultured murine neural progenitor cells, we show that our framework is consistent with the observed cell accumulation at positive defects and depletion at negative defects. In an in-vivo setting, we show that the defect configuration consisting of a bound +1 defect state, which is stabilized by activity, surrounded by two -1/2 defects can create a stationary ring configuration of tentacles, consistent with observations of a basal marine invertebrate Hydra.
Abstract: In the standard regression discontinuity setting, treatment assignment is based on whether a unit’s observable score (running variable) crosses a known threshold. We propose a two-stage method to estimate the treatment effect when the score is unobservable to the econometrician while the treatment status is known for all units. In the first stage, we use a statistical model to predict a unit’s treatment status based on a continuous synthetic score. In the second stage, we apply a regression discontinuity design using the predicted synthetic score as the running variable to estimate the treatment effect on an outcome of interest. We establish conditions under which the method identifies the local treatment effect for a unit at the threshold of the unobservable score, the same parameter that a standard regression discontinuity design with known score would identify. We also examine the properties of the estimator using simulations, and propose the use machine learning algorithms to achieve high prediction accuracy. Finally, we apply the method to measure the effect of an investment grade rating on corporate bond prices by any of the three largest credit ratings agencies. We find an average 1% increase in the prices of corporate bonds that received an investment grade as opposed to a non-investment grade rating.
Abstract: We will go through modern deep learning methods and existing approaches to their interpretation. Next, I will describe a graph neural network framework. You will also be introduced to an economic analogue of gravity. Finally, we will see how these tools can help understand observed trade flows between 181 countries over 68 years. [Joint work with Michael R. Douglas.]
Abstract: ‘t Hooft anomalies of quantum field theories (QFTs) with an invertible global symmetry G (including spacetime and internal symmetries) in a d-dim spacetime are known to be classified by a d+1-dim cobordism group TPd+1(G), whose group generator is a d+1-dim cobordism invariant written as a d+1-dim invertible topological field theory. Deformation class of QFT is recently proposed to be specified by its symmetry G and a d+1-dim invertible topological field theory. Seemly different QFTs of the same deformation class can be deformed to each other via quantum phase transitions. We ask which deformation class controls the 4d ungauged or gauged (SU(3)×SU(2)×U(1))/Zq Standard Model (SM) for q=1,2,3,6 with a continuous or discrete (B−L) symmetry and with also a compatible discrete baryon plus lepton Z_{2Nf} B+L symmetry. (The Z_{2Nf} B+L is discrete due to the ABJ anomaly under the BPST instanton.) We explore a systematic classification of candidate perturbative local and nonperturbative global anomalies of the 4d SM, including all these gauge and gravitational backgrounds, via a cobordism theory, which controls the SM’s deformation class. While many Grand Unified Theories violating the discrete B+L symmetry suffer from the proton decay, the SM and some versions of Ultra Unification (constrained by Z_{16} class global anomaly that replaces sterile neutrinos with new exotic gapped/gapless topological or conformal sectors) can have a stable proton. Dictated by a Z_2 class global mixed gauge-gravitational anomaly, there can be a gapless deconfined quantum critical region between Georgi-Glashow and Pati-Salam models — the Standard Model and beyond occur as neighbor phases. We will also comment on a new mechanism to give the neutrino mass via topological field theories and topological defects. Work based on arXiv:2112.14765, arXiv:2204.08393, arXiv:2202.13498 and references therein.
Abstract: In 1959 Paul Erdos and Alfred Renyi introduced a model of random graphs that is the cornerstone of modern probabilistic combinatorics. Now known as the “Erdos-Renyi” model of random graphs it has far-reaching applications in combinatorics, computer science, and other fields.
The model is defined as follows: Given a natural number $n$ and a parameter $p \in [0,1]$, let $G(n;p)$ be the distribution on graphs with $n$ vertices in which each of the $\binom{n}{2}$ possible edges is present with probability $p$, independent of all others. Despite their apparent simplicity, the study of Erdos-Renyi random graphs has revealed many deep and non-trivial phenomena.
A central feature is the appearance of threshold phenomena: For all monotone properties (e.g., connectivity and Hamiltonicity) there is a critical probability $p_c$ such that if $p >> p_c$ then $G(n;p)$ possesses the property with high probability (i.e., with probability tending to 1 as $n \to \infty$) whereas if $p << p_c$ then with high probability $G(n;p)$ does not possess the property. In this talk we will focus on basic properties such as connectivity and containing a perfect matching. We will see an intriguing connection between these global properties and the local property of having no isolated vertices. We will then generalize the Erdos-Renyi model to higher dimensions where many open problems remain.
Abstract: The standard model of cosmology is built on the fact that while viewed on a sufficiently coarse-grained scale the portion of our universe that is accessible to observation appears to be spatially homogeneous and isotropic. Therefore this observed `homogeneity and isotropy’ of our universe is not known to be dynamically derived. In this talk, I will present an interesting dynamical mechanism within the framework of the Einstein flow (including physically reasonable matter sources) which suggests that many closed manifolds that do not support homogeneous and isotropic metrics at all will nevertheless evolve to be asymptotically compatible with the observed approximate homogeneity and isotropy of the physical universe. This asymptotic spacetime is naturally isometric to the standard FLRW models of cosmology. In order to conclude to what extent the asymptotic state is physically realized, one needs to study its stability properties. Therefore, I will briefly discuss the stability issue and its consequences (e.g., structure formation, etc).
Abstract: One of the fundamental problems in mathematical relativity is the weak cosmic censorship conjecture, proposed by Penrose, which roughly states that for generic physical spacetime, the singularities (if existed) must be hidden behind the black holes. Unfortunately, the singularities visible to faraway observers, which are called by naked singularities, indeed exist. The first example constructed by Christodoulou in 1994 is a family of self-similar spherically symmetric spacetime, in which the naked singularity forms due to a self-gravitating scalar field. Therefore the suitable censorship conjecture should be reduced to prove the instability of the naked singularities. In 1999 Christodoulou succeeded to prove the weak cosmic censorship conjecture in spherically symmetric cases, and recently the co-author and I found that the corresponding results have a big probability to be extended to spacetime without symmetries. In this talk I will discuss how to prove the instability of naked singularities using the energy method, and it is this wild method that helps us to extend some results to the asymmetric cases.
Abstract: A knowledge graph (KG) is a data structure which represents entities and relations as the vertices and edges of a directed graph. Two examples are Wikidata for general knowledge and SemMedDB for biomedical data. A popular KG representation method is graph embedding, which facilitates question answering, inferring missing edges, and logical reasoning tasks. In this talk we introduce the topic and explain relevant mathematical results on graph embedding. We then analyze KG inference into several mechanisms: motif learning, network learning and unstructured statistical inference, and describe experiments to measure the contributions of each mechanism.
Joint work with M. Simkin, O. Ben-Eliezer, T. Wu, S. P. Chin, T. V. Dang and A. Wood.
Abstract: Discrete spacetime symmetries of parity P or reflection R, and time-reversal T, act naively as a Z2-involution on the spacetime coordinates; but together with a charge conjugation C and the fermion parity (−1)^F, these symmetries can be further fractionalized forming nonabelian C-P-R-T-(−1)^F group structures, in various examples such as relativistic Lorentz invariant Dirac spinor quantum field theories (QFT), or nonrelativistic quantum many-body systems (involving Majorana zero modes). This result answers Prof. Shing-Tung Yau’s question on “Can C-P-T symmetries be fractionalized more than involutions?” based on arxiv:2109.15320.
In the second part of my talk, I will sketch to explain how can we modify the so(10) Grand Unified Theory (GUT) by adding a new topological term such that two GUTs of Georgi-Glashow and Pati-Salam can smoother into each other in a quantum phase transition, where the Standard Model and new dark sector physics can occur naturally near the critical region. The new modified so(10) GUT requires a double Spin structure that we name DSpin. This phenomenon is inspired by the “deconfined quantum criticality” in condensed matter. Based on arxiv:2106.16248.
Abstract: Quantum field theories can often be used to uncover hidden algebraic structures in geometry and hidden geometric structures in algebra. In this talk, I will demonstrate how such “wall-crossing” can relate the moduli space of Higgs bundles with the moduli space of vortices.
Abstract: The complex Monge-Ampere equations occupies an central role in K\”ahler geometry, beginning with Yau’s famous solutions of the Calabi conjecture. Later developments has led to many interesting geometric applications and opening of new fields. In this talk, I will introduce the complex Monge-Ampere equation and discuss the interplay between their analysis and geometry, with a particular focus on the a priori C^0 estimates and their various applications. In the end, I will also try to discuss some recent work with B. Guo and D.H. Phong on a new approach for proving sharp C^0 estimates for complex Monge-Ampere equations, this new approach avoids the machinery of pluripotential theory that was previously necessary and has the advantage of generalizing to a large class of fully nonlinear equations.
Abstract: The first known construction of mirror pairs of Calabi-Yau manifolds was the Greene-Plesser “quotient and resolve” procedure which applies to pencils of hypersurfaces in projective space. We’ll review this approach, uncover the hints it gives for some more general mirror constructions, and describe a brand-new variant that applies to pencils of hypersurfaces in Grassmannians. This last is joint work with Tom Coates and Elana Kalashnikov (arXiv:2110.0727).
Abstract: In this talk, I will explain the overall situation of China’s financial industry and review the development of China’s financial regulatory system reform from 1949 to 2021. Then, I will explain the policies of the 3 stages of financial opening-up, 2001–08, 2008–18, 2018≠present. In particular, the latest round of opening-up from 2018 has brought great opportunities for foreign institutions. China has the world’s largest banking industry with assets totalling $53 trillion, and accounts for 1/3 of the growth in global insurance premiums over the next 10 years. I will also introduce the progress of research & development of China’s Central Bank Digital Currency (CBDC, or E-CNY). By October 2021, 140 million people had opened E-CNY wallets, and 1.6 million merchants could accept payments using eCNY wallets, including utilities, catering services, transportation, retail and government services.
Abstract: I will discuss old and new connections between black hole physics, 2D quantum gravity, and random matrix theory. Black holes are believed to be very complicated, strongly interacting quantum mechanical systems, and certain aspects of their Hamiltonians should be well approximated by random matrix theory. The near-horizon effective dynamics of near-extremal black holes is two-dimensional, and many theories of 2D quantum gravity are known to have random matrix descriptions. All of these expectations were recently borne out in surprising detail with the solution of the Jackiw-Teitelboim (JT) model, but this result raises more questions than it answers. If time permits, I will discuss some extensions of these results and possible future directions.
Abstract: Consider the discrete cube $\{-1,1\}^N$ and a random collection of half spaces which includes each half space $H(x) := \{y \in \{-1,1\}^N: x \cdot y \geq \kappa \sqrt{N}\}$ for $x \in \{-1,1\}^N$ independently with probability $p$. The solution space is the intersection of these half spaces. In this talk, we will talk about its sharp threshold phenomenon, the frozen structure of the solution space, and the Gardner formula.
During the 2021-22 academic year, the CMSA will be co-hosting a seminar on Swampland, with the Harvard Physics Department, organized by Miguel Montero, Cumrun Vafa, Irene Valenzuela. This seminar is a part of the Swampland Program. This seminar will take place on Mondays at 10:00 am – 11:30 am (Boston time). To learn how to attend, please subscribe here.
Abstract: The theory of topological modular forms leads to many interesting constraints and predictions for two-dimensional quantum field theories, and some of them might have interesting implications for the swampland program. In this talk, I will show that a conjecture by Segal, Stolz and Teichner requires the constant term of the partition function of a bosonic holomorphic CFTs to be divisible by specific integers determined by the central charge. We verify this constraint in large classes of physical examples, and rule out the existence of an infinite set of “extremal CFTs”, including those with central charges c = 48, 72, 96 and 120.
Abstract: A proposal to use the renormalisation group to address moduli stabilisation in IIB string perturbation theory will be described. We revisit brane-antibrane inflation combining this proposal with non-linearly realised supersymmetry.
4/5/2022
Simon Caron-Huot (McGill University) and Julio Parra (Caltech)
Abstract: We study constraints from causality and unitarity on 2→2 graviton scattering in four-dimensional weakly-coupled effective field theories. Together, causality and unitarity imply dispersion relations that connect low-energy observables to high-energy data. Using such dispersion relations, we derive two-sided bounds on gravitational Wilson coefficients in terms of the mass M of new higher-spin states. Our bounds imply that gravitational interactions must shut off uniformly in the limit G→0, and prove the scaling with M expected from dimensional analysis (up to an infrared logarithm). We speculate that causality, together with the non-observation of gravitationally-coupled higher-spin states at colliders, severely restricts modifications to Einstein gravity that could be probed by experiments in the near future.
Abstract: We revisit type IIB flux compactification that are mirror dual to type IIA on rigid Calabi-Yau manifolds. We find a variety of interesting new solutions, like fully stabilized Minkowski vacua and infinite families of AdS$_4$ solutions with arbitrarily large numbers of spacetime filling D3 branes. We discuss how these solutions fit into the web of swampland conjectures.
Abstract: I will explore the interplay between Swampland conjectures and models of inflation and light Dark Matter. To that end, I will briefly review the weak gravity conjecture (WGC) and the related Festina Lente (FL) bound. These have implications for light darkly and milli-charged particles and can disfavor a large portion of parameter space. The FL bound also implies strong restrictions on the field content of our universe during inflation and presents an opportunity for inflationary model building. At the same time, it rules out some popular models like chromo-natural inflation and gauge-flation. Finally, I will review another Swampland conjecture related to Stückelberg photon masses and discuss its implications for astro-particle physics.
Abstract: Motivated by a relationship between the Zamolodchikov and NLSM metrics to the so-called quantum information metric, I will discuss recent work (2106.11313) on understanding infinite distance limits within the context of information theory. I will describe how infinite distance points represent theories that are hyper-distinguishable, in the sense that they can be distinguished from “nearby” theories with certainty in relatively few measurements. I will then discuss necessary and sufficient ingredients for the appearance of these infinite distance points, illustrate these in simple examples, and describe how this perspective can help the swampland program.
Abstract: We construct supersymmetric AdS4 vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the α 0 expansion is likewise well-controlled. We find extremely small cosmological constants, with magnitude < 10^{-123} in Planck units. The compactifications are large, but not exponentially so, and hence these vacua manifest hierarchical scale-separation, with the AdS length exceeding the Kaluza-Klein length by a factor of a googol.
Abstract: In this talk I will introduce a particular formulation of the Weak Gravity Conjecture in AdS space in terms of the self-binding energy of a particle. The holographic CFT dual of this formulation corresponds to a certain convex-like structure for operators charged under continuous global symmetries. Motivated by this, we propose a conjecture that this convexity is a general property of all CFTs, not just those with weakly-curved gravitational duals. It is possible to test this in simple CFTs, the conjecture passes all the tests performed so far.
Abstract: I will explain what the Festina Lente bound means and where it comes from. Then I discuss its possible implications for phenomenology, both top-down and bottom-up.
Abstract: I describe our work looking at `traditional’ scenarios of moduli stabilisation from a holographic perspective. This reveals some interesting structure that is not apparent from the top-down perspective. For vacua in the extreme regions of moduli space, such as LVS in type IIB or the DGKT flux vacua in type IIA, the dual moduli conformal dimensions reduce to fixed values – in a certain sense, the low-conformal dimension part of the CFT is unique and independent of the large number of flux choices. For the DGKT flux vacua these conformal dimensions are also integer, for reasons we do not understand.
Abstract: Recently, a set of non-supersymmetric AdS_4 vacua of massive type IIA string theory has been constructed. These vacua are perturbatively stable with respect to the full KK spectrum of type mIIA supergravity and furthermore, they are stable against a variety of non-perturbative decay channels. Hence, at this point, they represent a serious challenge to the AdS swampland conjecture. In my talk, I will review in detail the construction of these vacua as well as introduce a new decay channel, ultimately sealing their fate as being unstable.
11/15/2021
Nima Arkani-Hamed (IAS), and Gary Shiu (UW-Madison)
This week’s seminar will be an open mic discussion which will be led by Nima Arkani-Hamed (IAS), and by Gary Shiu (UW-Madison), and the topic will be “Swampland constraints, Unitarity and Causality”. They will start with a brief introduction sharing their thoughts about the topic and moderate a discussion afterwards.
Abstract: In this talk I will introduce a generalized notion of finiteness that provides a structural principle for the set of effective theories that can be consistently coupled to quantum gravity. More concretely, I will propose a ‘tameness conjecture’ that states that all scalar field spaces and coupling functions that appear in such an effective theory must be definable in an o-minimal structure. The fascinating field of tame geometry has seen much recent progress and I will argue that the results can be used to support the above swampland conjecture. The strongest evidence arises from a new finiteness theorem for the flux landscape which is shown using the tameness of the period map.
Abstract: In this talk I will review massive type IIA flux compactifications that seem to give rise to infinite families of supersymmetric 4d AdS vacua. These vacua provide an interesting testing ground for the swampland program. After reviewing potential shortcomings of this setup, I will discuss recent progress on overcoming them and getting a better understanding of these solutions.
Abstract: Extremal black holes play a key role in our understanding of various swampland conjectures and in particular the WGC. The mild form of the WGC states that higher-derivative corrections should decrease the mass of extremal black holes at fixed charge. Whether or not this conjecture is satisfied depends on the sign of the combination of Wilson coefficients that control corrections to extremality. Typically, corrections to extremality need to be computed on a case-by-case basis, but in this talk I will present a universal derivation of extremal black hole corrections using the Iyer-Wald formalism. This leads to a formula that expresses general corrections to the extremality bound in terms of the stress tensor of the perturbations under consideration, clarifying the relation between the WGC and energy conditions. This shows that a necessary condition for the mild form of the WGC to be satisfied is a violation of the Dominant Energy Condition. This talk is based on 2111.04201.
Previous Quantum Matter/Condensed Matter Seminar schedule information and video links can be found here.
As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place Wednesdays from 10:30 – 12:00pm on Zoom. The Condensed Matter/Math Seminar will take place on Thursdays from 10:30 – 12:00pm on Zoom. In addition to the Quantum Matter seminar, the CMSA will also be hosting a related seminar series on a Strongly Correlated Quantum Materials and High-Temperature Superconductors. Please email the seminar organizer to obtain a link.
The schedules for both seminars will be updated below as speakers are confirmed:
Abstract: Metals that do not fit Landau’s famous Fermi liquid paradigm of quasiparticles are plentiful in experiments, but constructing their theoretical description is a major challenge in modern quantum many-body physics. I will describe new models that can systematically describe such non-Fermi liquid metals at quantum critical points, and that allow for the accurate computation of a whole host of experimentally measurable static and dynamic quantities despite the presence of both strong correlations and disorder. I will further demonstrate that disorder coupling to interaction operators can lead to the experimentally observed linear-in-temperature (T-linear) resistivity seen at metallic quantum critical points, and can also generate the observed universal “Planckian” transport scattering rate of kBT/ℏ. Finally, I will show that “perfect” T-linear resistivity is associated with an energy invariant quantity defined in the many-body microcanonical ensemble, which motivates the existence of a deep connection between the T-linear resistivity seen at high temperatures and low temperatures with the same slope in many quantum critical materials.
Abstract: In this talk, I will describe many-body quantum chaos in a recently proposed large-N theory for critical Fermi surfaces in two spatial dimensions, by computing out-of-time-order correlation functions. I will use the ladder identity proposed by Gu and Kitaev, and show that the chaos Lyapunov exponent in this system takes on the maximum possible value of 2πkBT/ℏ, where T is the absolute temperature. In addition, by varying the dynamic critical exponent, I will show that the maximal chaos persists only in the regime where quasiparticles are absent. When quasiparticles are present, the Lyapunov exponent scales with the temperature as ~ T^a, where a < 1, which is parametrically smaller than the maximal rate.
Abstract: I will introduce a class of non-invertible topological defects in (3 + 1)d gauge theories whose fusion rules are the higher-dimensional analogs of those of the Kramers-Wannier defect in the (1 + 1)d critical Ising model. As in the lower-dimensional case, the presence of such non-invertible defects implies self-duality under a particular gauging of their discrete (higher-form) symmetries. Examples of theories with such a defect include SO(3) Yang-Mills (YM) at θ = π, N = 1 SO(3) super YM, and N = 4 SU(2) super YM at τ = i. I will also explain an analogous construction in (2+1)d, and give a number of examples in Chern-Simons-matter theories. This talk is based on https://arxiv.org/abs/2111.01141.
Abstract: In metals, orbital motions of conduction electrons are quantized in magnetic fields, which is manifested by quantum oscillations in electrical resistivity. This Landau quantization is generally absent in insulators, in which all the electrons are localized. Here we report a notable exception in an insulator — ytterbium dodecaboride (YbB12). The resistivity of YbB12, despite much larger than that of usual metals, exhibits profound quantum oscillations under intense magnetic fields. This unconventional oscillation is shown to arise from the insulating bulk instead of conducting surface states. The large effective masses indicate strong correlation effects between electrons. Our result is the first discovery of quantum oscillations in the electrical resistivity of a strongly correlated insulator and will bring crucial insight into understanding the ground state in gapped Kondo systems.
Abstract: Superstring theory as we know it started from the discovery by Green and Schwarz in 1984 that the perturbative anomalies of heterotic strings miraculously cancel. But the cancellation of global anomalies of heterotic strings remained an open problem for a long time.In this talk, I would like to report how this issue was finally resolved last year, by combining two developments outside of string theory. Namely, on one hand, the study of topological phases in condensed matter theory has led to our vastly improved understanding of the general form of global anomalies. On the other hand, the study of topological modular forms in algebraic topology allows us to constrain the data of heterotic worldsheet theories greatly, as far as their contributions to the anomalies are concerned. Putting them together, it is possible to show that global anomalies of heterotic strings are always absent.The talk is based on https://arxiv.org/abs/2103.12211 and https://arxiv.org/abs/2108.13542 , in collaboration with Mayuko Yamashita.
Abstract: It is well-established that the Standard Model (SM) of particle physics is based on su(3)Xsu(2)Xu(1) Lie-algebra. What is less appreciated, however, is that SM accommodates a Z_6 1-form global symmetry. Gauging this symmetry, or a subgroup of it, changes the global structure of the SM gauge group and amounts to summing over sectors of instantons with fractional topological charges. After a brief review of the concept of higher-form symmetries, I will explain the origin of the Z_6 1-form symmetry and construct the explicit fractional-instanton solutions on compact manifolds. The new instantons mediate baryon-number and lepton-number violating processes, which can win over the weak BPST-instanton processes, provided that SM accommodates extra hyper-charged particles above the TeV scale. I will also comment on the cosmological aspects of the new solutions.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: ‘tHooft anomalies of anomalous systems can be described via anomaly inflow by invertible theories living in one dimension higher. Thanks to this it is possible to provide a general method to determine modular transformations of anomalous 2d fermionic CFTs with general discrete symmetry group $G^f$. As a by-product, one is able to determine explicit combinatorial expressions of spin-cobordism invariants in terms of Dehn-surgery representation of 3-manifolds. The same techniques also provide a method for evaluating the map from the group classifying free fermionic anomalies to the group of anomalies in interacting theories. As examples, we work out the details for some symmetry groups, including non-abelian ones, and, as an application, we use these results to bootstrap the spectrum of the theories with a given anomaly.
Abstract: In this sequence of talks, I will describe our work with Alexander Frenkel and Stephen Randall, in which we presented a novel topological quantum gravity, relating three previously unrelated fields: Topological quantum field theories (of the cohomological type), the theory of Ricci flows on Riemannian manifolds, and nonrelativistic quantum gravity. The remarkable richness of results produced in the recent decades by mathematicians studying the Ricci flow promises to shed new light on the physics of the path integral in quantum gravity (at least in the topological regime). In the opposite direction, the techniques of quantum field theory and path integrals may end up putting some of the mathematical results in the Ricci flow theory in a new perspective as well.
Abstract: Three-dimensional (3d) gapped topological phases with fractional excitations are divided into two subclasses: One has topological order with point-like and loop-like excitations fully mobile in the 3d space, and the other has fracton order with point-like excitations constrained in lower-dimensional subspaces. These exotic phases are often studied by exactly solvable Hamiltonians made of commuting projectors, which, however, are not capable of describing those with chiral gapless surface states. Here we introduce a systematic way, based on cellular construction recently proposed for 3d topological phases, to construct another type of exactly solvable models in terms of coupled quantum wires with given inputs of cellular structure, two-dimensional Abelian topological order, and their gapped interfaces. We show that our models can describe both 3d topological and fracton orders and even their hybrid and study their universal properties such as quasiparticle statistics and topological ground-state degeneracy.
Abstract: We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase “w2w3” in (4+1)D that has an anomalous boundary topological order with fermionic particle and fermionic loop excitations that have mutual statistics. Finally, we will demonstrate a few examples of fermionic loop excitations.
Abstract: In this talk we will discuss the interaction between magnetic monopoles and massless fermions. In the 1980’s Callan and Rubakov showed that in the simplest example and that fermion-monopole interactions catalyze proton decay in GUT completions of the standard model. Here we will explain how fermions in general representations interact with general spherically symmetric monopoles and classify the types of symmetries that are broken: global symmetries with ABJ-type anomalies.
Abstract: Motivated by a puzzle arising from recent work on staggered lattice fermions we introduce Kaehler-Dirac fermions and describe their connection both to Dirac fermions and staggered fermions. We show that they suffer from a gravitational anomaly that breaks a chiral U(1) symmetry specific to Kaehler-Dirac fermions down to Z_4 in any even dimension. In odd dimensions we show that the effective theory that results from integrating out massive Kaehler-Dirac fermions is a topological gravity theory. Such theories generalize Witten’s construction of (2+1) gravity as a Chern Simons theory. In the presence of a domain wall massless modes appear on the wall which can be consistently coupled to gravity due to anomaly inflow from the bulk gravitational theory. Much of this story parallels the usual discussion of topological insulators. The key difference is that the twisted chiral symmetry and anomaly structure of Kaehler-Dirac theories survives intact under discretization and governs the behavior of the lattice models. $Z_4$ invariant four fermion interactions can be used to gap out states in such theories without breaking symmetries and in flat space yields the known constraints on the number of Majorana fermions needed symmetric mass generation namely eight and sixteen Majorana spinors in two and four dimensions.
Abstract: We present computations of the thermal Hall coefficient of phonons scattering off defects with multiple energy levels. Using a microscopic formulation based on the Kubo formula, we find that the leading contribution perturbative in the phonon-defect coupling is of the `side-jump’ type, which is proportional to the phonon lifetime. This contribution is at resonance when the phonon energy equals a defect level spacing. Our results are obtained for different defect models, and include models of an impurity quantum spin in the presence of quasi-static magnetic order with an isotropic Zeeman coupling to the applied field. This work is based on arxiv: 2201.11681
Abstract: Some recent work in the quantum gravity literature has considered what happens when the amplitudes of a TQFT are summed over the bordisms between fixed in-going and out-going boundaries. We will comment on these constructions. The total amplitude, that takes into account all in-going and out-going boundaries can be presented in a curious factorized form. This talk reports on work done with Anindya Banerjee and is based on the paper on the e-print arXiv 2201.00903.
Abstract: The Swampland program aims at uncovering the universal implications of quantum gravity at low-energy physics. I will review the basic ideas of the Swampland program, formal and phenomenological implications, and provide a survey of the techniques commonly used in Swampland research including tools from quantum information, holography, supersymmetry, and string theory.
Abstract: I will show that a quantum state in a lattice spin (boson) system must be long-range entangled if it has non-zero lattice momentum, i.e. if it is an eigenstate of the translation symmetry with eigenvalue not equal to 1. Equivalently, any state that can be connected with a non-zero momentum state through a finite-depth local unitary transformation must also be long-range entangled. The statement can also be generalized to fermion systems. I will then present two applications of this result: (1) several different types of Lieb-Schultz-Mattis (LSM) theorems, including a previously unknown version involving only a discrete Z_n symmetry, can be derived in a simple manner; (2) a gapped topological order (in space dimension d>1) must weakly break translation symmetry if one of its ground states on torus has nontrivial momentum – this generalizes the familiar physics of Tao-Thouless in fractional quantum Hall systems.
Abstract: I will talk about the edge physics of the deconfined quantum phase transition (DQCP) between a spontaneous quantum spin Hall (QSH) insulator and a spin-singlet superconductor (SC). Although the bulk of this transition is in the same universality class as the paradigmatic deconfined Neel to valence-bond-solid transition, the boundary physics has a richer structure due to proximity to a quantum spin Hall state. We use the parton trick to write down an effective field theory for the QSH-SC transition in the presence of a boundary and calculate various edge properties in a large-N limit. We show that the boundary Luttinger liquid in the QSH state survives at the phase transition, but only as fractional degrees of freedom that carry charge but not spin. The physical fermion remains gapless on the edge at the critical point, with a universal jump in the fermion scaling dimension as the system approaches the transition from the QSH side. The critical point could be viewed as a gapless analogue of the QSH state but with the full SU(2) spin rotation symmetry, which cannot be realized if the bulk is gapped. This talk reports on the work done with Liujun Zou and Chong Wang (arxiv:2110.08280).
Abstract: We show that Polchinski’s equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This gives a surprising information- theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. We will provide reviews of both the exact renormalization group, as well as the theory of optimal transportation. Our results allow us to establish a new, non-perturbative RG monotone, and also reformulate RG flow as a variational problem. The latter enables new numerical techniques and allows us to establish a systematic connection between neural network methods and RG flows of conventional field theories. Our techniques generalize to other RG flow equations beyond Polchinski’s.
Abstract: Characterizing many-body entanglement is one of the most important problems in quantum physics. We present our studies on the steady state von Neumann entropy and its transition in Brownian SYK models. For unitary evolution, we show that the correlations between different replicas account for the Page curve at late time, and a permutation group structure emerges in the large-N calculation. In the presence of measurements, we find a transition of von Neumann entropy from volume-law to area-law by increasing the measurement rate. We show that a proper replica limit can be taken, which shows that the transition occurs at the point of replica symmetry breaking.
4/7/2022
Jung Hoon Han (Sungkyunkwan University, Suwon, South Korea)
Abstract: Exactly solvable spin models such as toric codes and X-cube model have heightened our understanding of spin liquids and topological matter in two and three dimensions. Their exact solvability, it turns out, is rooted in the existence of commuting generators in their parent lattice gauge theory (LGT). We can understand the toric codes as Higgsed descendants of the rank-1 U(1) LGT in two and three dimensions, and the X-cube model as that of rank-2 U(1) LGT in three dimensions. Furthermore, the transformation properties of the gauge fields in the respective LGT is responsible for, and nearly determines the structure of the effective field theory (EFT) of the accompanying matter fields. We show how to construct the EFT of e and m particles in the toric codes and of fractons and lineons in the X-cube model by following such an idea. Recently we proposed some stabilizer Hamiltonians termed rank-2 toric code (R2TC) and F3 model (3D). We will explain what they are, and construct their EFTs using the gauge principle as guidance. The resulting field theory of the matter fields are usually highly interacting and exhibit unusual conservation laws. Especially for the R2TC, we demonstrate the existence of what we call the “dipolar braiding statistics” and outline the accompanying field theory which differs from the usual BF field theory of anyon braiding.
References: [1] “Model for fractions, fluxons, and free verte excitations”, JT Kim, JH Han, Phys. Rev. B 104, 115128 (2021) [1] “Rank-2 toric code in two dimensions”, YT Oh, JT Kim, EG Moon, JH Han, Phys. Rev. B 105, 045128 (2022) [2] “Effective field theory for the exactly solvable stabilizer spin models”, JT Kim, YT Oh, JH Han, in preparation. [3] “Effective field theory of dipolar braiding statistics in two dimensions”, YT Oh, JT Kim, JH Han, in preparation.
Abstract: It has been known that the four-dimensional abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg- Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg-Wilson fermions, it has been argued that the mirror fermions do not decouple: in the 3450 model with Dirac- and Majorana-Yukawa couplings to XY-spin field, the two- point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the so-called ParaMagnetic Strong-coupling(PMS) phase.
We re-examine why the attempt seems a “Mission: Impossible” in the 3450 model. We point out that the effective operators to break the fermion number symmetries (’t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana-Yukawa couplings. We also observe that the type of Majorana-Yukawa term considered there is singular in the large limit due to the nature of the chiral projection of the Ginsparg-Wilson fermions, but a slight modification without such singularity is allowed by virtue of the very nature.
We then consider a simpler four-flavor axial gauge model, the 14(-1)4 model, in which the U(1)A gauge and Spin(6)( SU(4)) global symmetries prohibit the bilinear terms, but allow the quartic terms to break all the other continuous mirror-fermion symmetries. This model in the weak gauge-coupling limit is related to the eight-flavor Majorana Chain with a reduced SO(6)xSO(2) symmetry in Euclidean path-integral formulation. We formulate the model so that it is well-behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte-Carlo simulations in the weak gauge-coupling limit, we show a numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows a regular local behavior.
Finally, by gauging a U(1) subgroup of the U(1)A× Spin(6)(SU(4)) of the previous model, we formulate the 21(−1)3 chiral gauge model and argue that the induced effective action in the mirror sector satisfies the required locality property. This gives us “A New Hope” for the mission to be accomplished.
Abstract: I will explain a mechanism to cancel the vacuum energy and both terms in the Weyl anomaly in the standard model of particle physics, using conformally-coupled dimension-zero scalar fields. Remarkably, given the standard model gauge group SU(3)xSU(2)xU(1), the cancellation requires precisely 48 Weyl spinors — i.e. three generations of standard model fermions, including right-handed neutrinos. Moreover, the scalars possess a scale-invariant power spectrum, suggesting a new explanation for the observed primordial density perturbations in cosmology (without the need for inflation).As context, I will also introduce a related cosmological picture in which this cancellation mechanism plays an essential role. Our universe seems to be dominated by radiation at early times, and positive vacuum energy at late times. Taking the symmetry and analyticity properties of such a universe seriously suggests a picture in which spacetime has two sheets, related by a symmetry that, in turn, selects a preferred (CPT-symmetric) vacuum state for the quantum fields that live on the spacetime. This line of thought suggests new explanations for a number of observed properties of the universe, including: its homogeneity, isotropy and flatness; the arrow of time; several properties of the primordial perturbations; and the nature of dark matter (which, in this picture, is a right-handed neutrino, radiated from the early universe like Hawking radiation from a black hole). It also makes a number of testable predictions.(Based on recent, and ongoing, work with Neil Turok: arXiv:1803.08928, arXiv:2109.06204, arXiv:2110.06258, arXiv:2201.07279.)
4/20/2022 11:30–1:00 pm ET
Harold Y. Hwang (Stanford University & SLAC National Accelerator Laboratory)
Abstract: Since its discovery, unconventional superconductivity in cuprates has motivated the search for materials with analogous electronic or atomic structure. We have used soft chemistry approaches to synthesize superconducting infinite layer nickelates from their perovskite precursor phase. We will present the synthesis and transport properties of the nickelates, observation of a doping-dependent superconducting dome, and our current understanding of their electronic and magnetic structure.
Abstract: The Higgs phase of a gauge theory is important to both fundamental physics (e.g., electroweak theory) as well as condensed matter systems (superconductors and other emergent phenomena). However, such a charge condensate seems subtle and is sometimes described as the spontaneous breaking of gauge symmetry (or a global subgroup). In this talk, I will argue that the Higgs phase is best understood as a symmetry-protected topological (SPT) phase. The concept of SPT phases arose out of the condensed matter community, to describe systems with short-range entanglement and edge modes which cannot be removed in the presence of certain symmetries. The perspective that the Higgs phase is an SPT phase recovers known properties of the Higgs phase and provides new insights. In particular, we revisit the Fradkin-Shenker model and the distinction between the Higgs and confined phases of a gauge theory.
Abstract: We will overview the program of geometrically engineering four dimensional supersymmetric QFTs as compactifications of six dimensional SCFTs. In particular we will discuss how strong coupling phenomena in four dimensions, such as duality and emergence of symmetry, can be better understood in such geometric constructions.
Abstract: We are familiar with the idea that quantum gravity in AdS can holographically emerge from complex patterns of entanglement, but can the physics of big bang cosmology emerge from a quantum many-body system? In this talk I will argue that standard tools of holography can be used to describe fully non-perturbative microscopic models of cosmology in which a period of accelerated expansion may result from the positive potential energy of time-dependent scalar fields evolving towards a region with negative potential. In these models, the fundamental cosmological constant is negative, and the universe eventually recollapses in a time-reversal symmetric way. The microscopic description naturally selects a special state for the cosmology. In this framework, physics in the cosmological spacetime is dual to the vacuum physics in a static planar asymptotically AdS Lorentzian wormhole spacetime, in the sense that the background spacetimes and observables are related by analytic continuation. The dual spacetime is weakly curved everywhere, so any cosmological observables can be computed in the dual picture via effective field theory without detailed knowledge of the UV completion or the physics near the big bang. Based on 2203.11220 with S. Antonini, P. Simidzija, and M. Van Raamsdonk.
Abstract: The CDF collaboration recently reported a new precise measurement of the W boson mass MW with a central value significantly larger than the SM prediction. We explore the effects of including this new measurement on a fit of the Standard Model (SM) to electroweak precision data. We characterize the tension of this new measurement with the SM and explore potential beyond the SM phenomena within the electroweak sector in terms of the oblique parameters S, T and U. We show that the large MW value can be accommodated in the fit by a large, nonzero value of U, which is difficult to construct in explicit models. Assuming U = 0, the electroweak fit strongly prefers large, positive values of T. Finally, we study how the preferred values of the oblique parameters may be generated in the context of models affecting the electroweak sector at tree- and loop-level. In particular, we demonstrate that the preferred values of T and S can be generated with a real SU(2)L triplet scalar, the humble swino, which can be heavy enough to evade current collider constraints, or by (multiple) species of a singlet-doublet fermion pair. We highlight challenges in constructing other simple models, such as a dark photon, for explaining a large MW value, and several directions for further study.
Abstract: Recent advances in our understanding of symmetry in quantum many-body systems offer the possibility of a generalized Landau paradigm that encompasses all equilibrium phases of matter. This talk will be an elementary review of some of these developments, based on: https://arxiv.org/abs/2204.03045
Abstract: The cosmological lithium problem—that the observed primordial abundance is lower than theoretical expectations by order one—is perhaps the most statistically significant anomaly of SM+ ΛCDM, and has resisted decades of attempts by cosmologists, nuclear physicists, and astronomers alike to root out systematics. We upgrade a discrete subgroup of the anomaly-free global symmetry of the SM to an infrared gauge symmetry, and UV complete this at a scale Λ as the familiar U(1)_{B-N_cL} Abelian Higgs theory. The early universe phase transition forms cosmic strings which are charged under the emergent higher-form symmetry of the baryon minus lepton BF theory. These topological defects catalyze interactions which turn N_g baryons into N_g leptons at strong scale rates in an analogue of the Callan-Rubakov effect, where N_g=3 is the number of SM generations. We write down a model in which baryon minus lepton strings superconduct bosonic global baryon plus lepton number currents and catalyze solely 3p^+ → 3e^+. We suggest that such cosmic strings have disintegrated O(1) of the lithium nuclei formed during Big Bang Nucleosynthesis and estimate the rate, with our benchmark model finding Λ ~ 10^8 GeV gives the right number density of strings.
Abstract: We study a model for explaining the apparent deviation of the muon anomalous magnetic moment, (g-2), from the Standard Model expectation. There are no new scalars and hence no new hierarchy puzzles beyond those associated with the Standard model Higgs; the only new particles that are relevant for (g-2) are vector-like singlet and doublet leptons. Interestingly, this simple model provides a calculable example violating the Wilsonian notion of naturalness: despite the absence of any symmetries prohibiting its generation, the coefficient of the naively leading dimension-six operator for (g−2) vanishes at one-loop. While effective field theorists interpret this either as a surprising UV cancellation of power divergences, or as a delicate cancellation between matching UV and calculable IR corrections to (g−2) from parametrically separated scales, there is a simple explanation in the full theory: the loop integrand is a total derivative of a function vanishing in both the deep UV and IR. The leading contribution to (g−2) arises from dimension-eight operators, and thus the required masses of new fermions are lower than naively expected, with a sizable portion of parameter space already covered by direct searches at the LHC. All of the the viable parameter can be probed by the LHC and planned future colliders.
Abstract: This talk, in two parts, will discuss two (unrelated) instances of exotic quantum matter. In the first part, I will discuss quantum critical points describing possible transitions out of the Dirac spin liquid, towards either symmetry-breaking phases or topologically ordered spin liquids. I will also comment on the role of instanton zero modes for symmetry breaking in parton gauge theories. In the second part, I will propose an extension of Bloch band theory to hyperbolic lattices, such as those recently realized in circuit QED experiments, based on ideas from algebraic geometry and Riemann surface theory.
Abstract: Understanding the fluctuations of observables is one of the main goals in physics. We investigate such fluctuations when a subregion of the full system can be observed, focusing on geometries with corners. We report that the dependence on the opening angle is super-universal: up to a numerical prefactor, this function does not depend on anything, provided the system under study is uniform, isotropic, and correlations do not decay too slowly. The prefactor contains important physical information: we show in particular that it gives access to the long-wavelength limit of the structure factor. We illustrate our findings with several examples: classical fluids, fractional quantum Hall (FQH) states, scale invariant quantum critical theories, and metals. Finally, we discuss connections with the entanglement entropy, including new results for Laughlin FQH states.
Abstract: We present a model of quantum gravity in which dimension, topology and geometry of spacetime are collective dynamical variables that describe the pattern of entanglement of underlying quantum matter. As spacetimes with arbitrary dimensions can emerge, the gauge symmetry is generalized to a group that includes diffeomorphisms in general dimensions. The gauge symmetry obeys a first-class constraint operator algebra, and is reduced to a generalized hypersurface deformation algebra in states that exhibit classical spacetimes. In the semi-classical limit, we find a saddle-point solution that describes a series of (3+1)-dimensional de Sitter-like spacetimes with the Lorentzian signature bridged by Euclidean spaces in between.
Abstract: In this follow-up to Hitoshi Murayama’s talk “Some Exact Results in QCD-like and Chiral Gauge Theories”, I present a detailed analysis of the phases of $SO(N_c)$ gauge theory. Starting with supersymmetric $SO(N_c)$ with $N_F$ flavors, we extrapolate to the non-supersymmetric limit using anomaly-mediated supersymmetry breaking (AMSB). Interestingly, the abelian Coulomb and free magnetic phases do not survive supersymmetry breaking and collapse to a confining phase. This provided one of the first demonstrations of true confinement with chiral symmetry breaking in a non-SUSY theory.
Abstract: I will present a new mechanism and an exact theory of electron pairing due to repulsive interaction in doped insulators. When the kinetic energy is small, the dynamics of adjacent electrons on the lattice is strongly correlated. By developing a controlled kinetic energy expansion, I will show that two doped charges can attract and form a bound state, despite and because of the underlying repulsion. This attraction by repulsion is enabled by the virtual excitation of a third electron in the filled band. This three-particle pairing mechanism leads to a variety of novel phenomena at finite doping, including spin-triplet superconductivity, pair density wave, BCS-BEC crossover and Feshbach resonance involving “trimers”. Possible realizations in moire materials, ZrNCl and WTe2 will be discussed.
[1] V. Crepel and L. Fu, Science Advances 7, eabh2233 (2021) [2] V. Crepel and L. Fu, arXiv:2103.12060 [3] K. Slagle and L. Fu, Phys. Rev. B 102, 235423 (2020)
Abstract: We demonstrate that all known formulae for the thermal partition function for large N Chern Simons matter theory admit a simple Hilbert Space interpretation. In each case this quantity equals the partition function of an associated ungauged large $N$ matter theory with a particular local Lagrangian with one additional element: the Fock Space of this associated theory is projected down to the subspace of its WZW singlets. This projection, in particular, implies the previously encountered `Bosonic Exclusion Principle’, namely that no single particle state can be occupied by more than $k_B$ particles ($k_B$ is the Chern Simons level). Unlike its Gauss Law counterpart, the WZW constraint does not trivialize in the large volume limit. However thermodynamics does simplify in this limit; the final partition function reduces to a product of partition functions associated with each single particle state. These individual single particle state partition functions are a one parameter generalizations of their free boson and free fermion counterparts, and reduce to the later at extreme values of the ‘t Hooft coupling. At generic values of the rank and the level the occupation statistics of each energy level is given by a $q$ deformation of the usual free formulae of Bose and Fermi statistics.
Abstract: In this talk, I will review a recently developed strong coupling theory of magic-angle twisted bilayer graphene. An advantage of this approach is that a single formulation can capture both the insulating and superconducting states, and with a few simplifying assumptions, can be treated analytically. I begin by reviewing the electronic structure of magic angle graphene’s flat bands, in a limit that exposes their peculiar band topology and geometry. I will show how similarities between the flat bands and the lowest Landau level can provide valuable insights into the effect of interactions and form the basis for an analytic treatment of the problem. At integer fillings, this approach points to flavor ordered insulators, which can be captured by a sigma-model in its ordered phase. Remarkably, topological textures of the sigma model carry electric charge which enables the same theory to describe the doped phases away from integer filling. I will show how this approach can lead to superconductivity on disordering the sigma model, and estimate the Tc for the superconductor. I will highlight the important role played by an effective super-exchange coupling both in pairing and in setting the effective mass of Cooper pairs. At the end, I will show how this theory provides criteria to predict which multilayer graphene stacks are expected to superconduct including the recently discovered alternating twist trilayer platform.
Abstract: I will discuss ideas around symmetry and Wick rotation contained in joint work with Mike Hopkins (https://arxiv.org/abs/1604.06527). This includes general symmetry types for relativistic field theories and their Wick rotation. I will then indicate how the basic CRT theorem works for general symmetry types, focusing on the case of the pin groups. In particular, I expand on a subtlety first flagged by Greaves-Thomas.
Abstract: I start with a general map of gauge topology, including monopoles, instantons and instanton-dyons. Then comes reminder of the “topological landscape”, the minimal energy gauge field configurations, as a function of Chern-Simons number Ncs and r.m.s. size. It includes “valleys” at integer Ncs separated by mountain ridges. The meaning of instantons, instanton-antiinstanton “streamlines” or thimbles, and sphalerons are reminded, together with some proposal to produce sphalerons at LHC and RHIC.
Applications of instanton ensembles, as a model of QCD vacuum, are mostly related to their fermionic zero modes and t’Hooft effective Lagrangian, which explains explicit and spontaneous breaking of chiral symmetries. Recent applications are related with hadronic wave functions, at rest and in the light front (LFWFs). Two application would be spin-dependent forces and the so called “flavor asymmetry of antiquark sea” of the nucleons. At temperatures comparable to deconfinement transition, instantons get split into constituents called instanton-dyons. Studies of their ensemble explains both deconfinement and chiral transitions, in ordinary and deformed QCD.
Abstract: The layered honeycomb magnet alpha-RuCl3 orders below 7 K in a zigzag phase in zero field. An in-plane magnetic field H||a suppresses the zigzag order at 7 Tesla, leaving a spin-disordered phase widely believed to be a quantum spin liquid (QSL) that extends to ~12 T. We have observed oscillations in the longitudinal thermal conductivity Kxx vs. H from 0.4 to 4 K. The oscillations are periodic in 1/H (with a break-in-slope at 7 T). The amplitude function is maximal in the QSL phase (7 –11.5 T). I will describe a benchmark for crystalline disorder, the reproducibility and intrinsic nature of the oscillations, and discuss implications for the QSL state. I will also show detailed data on the thermal Hall conductivity Kxy measured from 0.4 K to 10 K and comment on recent half-quantization results.
Abstract: I will discuss line defects in d-dimensional Conformal Field Theories (CFTs). In the first part of the talk, I will argue that the ambient CFT places nontrivial constraints on Renormalization Group (RG) flows on such line defects. I will show that the flow on line defects is consequently irreversible and furthermore a canonical decreasing entropy function exists. This construction generalizes the g theorem to line defects in arbitrary dimensions. In the second part of the talk, I will present some applications. In particular, I will discuss impurities with large isospin S for some O(3) symmetric theories in the epsilon expansion. For sufficiently large S diagrammatic perturbation theory breaks down, and these are studied in a semiclassical expansion at fixed epsilon S.
Abstract: I will discuss some perspectives on symmetry coming from the study of topological defects in quantum field theory. I will argue that we should take topological defects themselves to define the symmetries of QFT. This gives us a view of the “category of QFTs”. I will describe some examples of these “categorical symmetries”, their applications, and some open problems.
Abstract: In this talk we will discuss a method of anomaly resolution due to Wang-Wen-Witten in the special case of (1+1) dimensional theories. Briefly, for our purposes, Wang-Wen-Witten argued that an ill-defined anomalous orbifold [X/G] could be resolved by extending G to a larger group and adding suitable phases. We analyze this process from the perspective of decomposition, a property of (1+1)-dimensional theories with “one-form symmetries” first described in 2006. Examples of such theories include orbifolds with trivially-acting subgroups, of which the extensions of [X/G] are examples. After a review of decomposition, we will see that decomposition implies that in (1+1) dimensions, the Wang-Wen-Witten procedure results in orbifolds that are equivalent to disjoint unions of orbifolds of X by explicitly nonanomalous subgroups of G.
Abstract: I will talk about the integrability and chaos of 1+1d interacting chiral edge states, which may arise on the edge of 2+1d topological phases. We show that integrable chiral Luttinger liquid is not always a good low energy description of the edge states, and marginal interactions can significantly affect their spectrum and integrability. We first study N identical chiral Majorana fermion modes with random 4-fermion interactions, where we show that the system undergoes a transition from integrable to quantum chaotic as N increases. The large N limit defines a chiral SYK model where the Lyapunov exponent in the out-of-time-ordered correlation can be solved analytically. I will also present a chiral SY model consisting of N interacting SU(M)_1 WZW models, which host anyons and exhibits similar quantum chaos for Abelian anyons. Lastly, I will talk about the analytical and numerical study of the 4/3 FQH edge theory, which shows unusual behavior in its integrability.
Abstract: For any quantum system invariant under gauging a higher-form global symmetry, we construct a non-invertible topological defect by gauging in only half of spacetime. This generalizes the Kramers-Wannier duality line in 1+1 dimensions to higher spacetime dimensions. We focus on the case of a one-form symmetry in 3+1 dimensions and determine the fusion rule. From modular invariance and a direct analysis of one-form symmetry-protected topological phases, we show that the existence of certain kinds of duality defects is intrinsically incompatible with a trivially gapped phase. By further assuming time-reversal symmetry, we find that the presence of certain duality defects implies that the low-energy phase has to be gapless unless the one-form symmetry is spontaneously broken. We give an explicit realization of this duality defect in the free Maxwell theory where the duality defect is realized by a Chern-Simons coupling between the gauge fields from the two sides.
Abstract: Topological defects provide a modern perspective on symmetries in quantum field theory. They generalize the familiar invertible symmetries described by groups to non-invertible symmetries described by fusion categories. Such generalized symmetries are ubiquitous in quantum field theory and provide new constraints on renormalization group flows and the IR phase diagram. In this talk I’ll review some recent progress in identifying and understanding fusion category symmetries in 1+1d conformal field theories. Time permitting, I’ll also comment on higher dimensional generalizations.
Abstract: It is widely asserted that there is no such thing as a Majorana fermion in four Euclidean dimensions. This is a pity because we might like to study Majorana fermions using heat-kernel regularized path integrals or by lattice-theory computations, and these tools are only available in Euclidean signature. I will show that to the contrary there are natural definitions of Euclidean Majorana-Fermion path integrals in all dimensions, and that key issue is not whether the gamma matrices are real or not, but whether the time-reversal and/or charge conjugation matrices are symmetric or antisymmetric.
Abstract: “Moire” materials produced by stacking monolayers with small relative twist angles are of intense current interest for the range of correlated electron phenomena they exhibit. The quench of the kinetic energy means that the interacting physics is controlled by the interplay between the interaction scale and intrinsic quantum geometries of the flat band states, in particular the Berry curvature and the Fubini-Study metric, which are in general spatially non-uniform. We show that the analytical solution of the twisted bilayer graphene wavefunction in the chiral limit has a special band geometry, endowing the Brillouin zone with a complex structure. This talk focus on the origin of the momentum space complex structure, concrete models that realize it, and its implications to electron-electron interactions. We first show the momentum space complex structure in Chern number C=1 flatbands implies the Bloch wavefunction to exhibit an exact correspondence to the lowest Landau level in the dual momentum space [2]. We present a generalization of the Haldane pseudopotential concept to deal with interacting problems in these bands and discuss experimental implications [2]. We also present an analytically solvable multi-layer generalized chiral graphene model, which exhibits arbitrarily high Chern number and ideal quantum geometries [3]. Numerical studies of interacting particles indicate model fractional Chern insulators without Landau level analogues, characterized by exact degeneracies and infinite particle entanglement spectra gaps [3]. References:
[1] Jie Wang, Yunqin Zheng, Andrew J. Millis, Jennifer Cano (Phys. Rev. Research 3, 023155) [2] Jie Wang, Jennifer Cano, Andrew J. Millis, Zhao Liu, Bo Yang (arXiv: 2105.07491, to appear in PRL) [3] Jie Wang, Zhao Liu (arXiv: 2109.10325)
Abstract: We find that several non-integrable systems exhibit some exact eigenstates that span the energy spectrum from lowest to the highest state. In the AKLT Hamiltonian and in several others “special” non-integrable models, we are able to obtain the analytic expression of states exactly and to compute their entanglement spectrum and entropy to show that they violate the eigenstate thermalization hypothesis. This represented the first example of ETH violation in a non-integrable system; these types of states have gained notoriety since then as quantum Scars in the context of Rydberg atoms experiments. We furthermore show that the structure of these states, in most models where they are found is that of an almost spectrum generating algebra which we call Restricted Spectrum Generating Algebra. This includes the (extended) Hubbard model, as well as some thin-torus limits of Fractional Quantum Hall states. Yet in other examples, such as the recently found chiral non-linear Luttinger liquid, their structure is more complicated and not understood.
Abstract: We discuss multipartitions of the gapped ground states of (2+1)-dimensional topological liquids into three (or more) spatial regions that are adjacent to each other and meet at points. By considering the reduced density matrix obtained by tracing over a subset of the regions, we compute various correlation measures, such as entanglement negativity, reflected entropy, and associated spectra. We utilize the bulk-boundary correspondence to achieve such multipartitions and construct the reduced density matrix near the entangling boundaries. We find the fingerprints of topological liquid in these quantities, such as (universal pieces in) the scaling of the entanglement negativity, and a non-trivial distribution of the spectrum of the partially transposed density matrix.
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).Watch Video on Youtube
Abstract: In this talk I will give an overview of semi-recent work with Hirosi Ooguri arguing that three old conjectures about symmetry in quantum gravity are true in the AdS/CFT correspondence. These conjectures are 1) that there are no global symmetries in quantum gravity, 2) that dynamical objects transforming in all irreducible representations of any gauge symmetry must exist, and 3) all internal gauge symmetries must be compact. Along the way I will need to carefully define what we mean by gauge and global symmetries in quantum field theory and quantum gravity, which leads to interesting applications in various related fields. These definitions will be the focus of the first talk, while the second will apply them to AdS/CFT to prove conjectures 1-3).
Abstract: I will describe some of my recent work on defects in supersymmetric field theories. The first part of my talk is focused on line defects in certain large classes of 4d N=2 theories and 3d N=2 theories. I will describe geometric methods to compute the ground states spectrum of the bulk-defect system, as well as implications on the construction of link invariants. In the second part I will talk about some perspectives of surface defects in 4d N=2 theories and related applications on the exact WKB method for ordinary differential equations. This talk is based on past joint work with A. Neitzke, various work in progress with D. Gaiotto, S. Jeong, A. Khan, G. Moore, as well as work by myself.
Abstract: Quasiparticle excitations in 3 + 1 dimensions can be either bosons or fermions. In this work, we introduce the notion of fermionic loop excitations in 3 + 1 dimensional topological phases. Specifically, we construct a new many-body lattice invariant of gapped Hamiltonians, the loop self-statistics μ = ±1, that distinguishes two bosonic topological orders that both superficially resemble 3 + 1d Z2 gauge theory coupled to fermionic charged matter. The first has fermionic charges and bosonic Z2 gauge flux loops (FcBl) and is just the ordinary fermionic toric code. The second has fermionic charges and fermionic loops (FcFl) and, as we argue, can only exist at the boundary of a non-trivial 4 + 1d invertible phase, stable without any symmetries i.e., it possesses a gravitational anomaly. We substantiate these claims by constructing an explicit exactly solvable 4 + 1d Walker–Wang model and computing the loop self-statistics in the fermionic Z2 gauge theory hosted at its boundary. We also show that the FcFl phase has the same gravitational anomaly as all-fermion quantum electrodynamics. Our results are in agreement with the recent classification of nondegenerate braided fusion 2- categories, and with the cobordism prediction of a non-trivial Z2-classified 4+1d invertible phase with action S = (1/2) w2 w3.
Title: Ultra Unification: Quantum Fields Beyond the Standard ModelAbstract: Strong, electromagnetic, and weak forces were unified in the Standard Model (SM) with spontaneous gauge symmetry breaking. These forces were further conjectured to be unified in a simple Lie group gauge interaction in the Grand Unification (GUT). Here I propose a theory beyond the SM and GUT by adding new gapped Topological Phase Sectors consistent with the nonperturbative global anomaly cancellation and cobordism constraints (especially from the baryon minus lepton number B – L, the electroweak hypercharge Y, and the mixed gauge-gravitational anomaly). Gapped Topological Phase Sectors are constructed via symmetry extension, whose low energy contains unitary Lorentz invariant topological quantum field theories (TQFTs): either 3+1d non-invertible TQFT (long-range entangled gapped phase), or 4+1d invertible or non-invertible TQFT (short-range or long-range entangled gapped phase). Alternatively, there could also be right-handed neutrinos, or gapless unparticle conformal field theories, or their combinations to altogether cancel the anomaly. We propose that a new high-energy physics frontier beyond the conventional 0d particle physics relies on the new Topological Force and Topological Matter including gapped extended objects (gapped 1d line and 2d surface operators or defects, etc., whose open ends carry deconfined fractionalized particle or anyonic string excitations). I will also fill in the dictionary between math, QFT, and condensed matter terminology, and elaborate on the global anomalies of Z2, Z4, Z16 classes useful for beyond SM. Work is based on arXiv:2012.15860, arXiv:2008.06499, arXiv:2006.16996, arXiv:1910.14668.
Abstract: Topological orders are gapped quantum liquid states without any symmetry. Most of their properties can be captured by investigating topological defects and excitations of various dimensions. Topological defects in n dimensions naturally form a (weak) n-category. In particular, anomalous topological order (boundary theory) is described by fusion n-category and anomaly-free topological order (bulk) is described by non-degenerate braided fusion n-category. Holographic principle works for topological orders: boundary always has a unique bulk. Another important property in 3+1D or higher is that point-like excitations must have trivial statistics; they must carry representations of a certain group. Such a “gauge group” is hidden in every higher dimensional topological order. In 3+1D, condensing point-like excitations leads to a canonical boundary which in turn determines the bulk topological order. By studying this boundary, a rather simple classification is obtained: 3+1D topological orders are classified by the above “gauge group” together with some cocycle twists. These ideas would also play an important role in dimensions higher than 3+1D and in the study of higher categories, topological quantum field theories and other related subjects.
Abstract: The theory of quantum phase transitions separating different phases with distinct symmetry patterns at zero temperature is one of the foundations of modern quantum many-body physics. In this talk, I will demonstrate that the existence of a 2D topological phase transition between a higher-order topological insulator (HOTI) and a trivial Mott insulator with the same symmetry eludes this paradigm. A significant new element of our phase transition theory is that the infrared (IR) effective theory is controlled by short wave-length fluctuations so the critical phenomenon is beyond the renormalization perspective.
6/10/2021
Theo Johnson-Freyd (Dalhousie U and Perimeter Institute)
Abstract: Braided fusion categories arise as the G-invariant (extended) observables in a 2+1D topological order, for some (generalized) symmetry group G. A minimal nondegenerate extension exists when the G-symmetry can be gauged. I will explain what this has to do with the classification of 3+1D topological orders. I will also explain a resolution to a 20-year-old question in mathematics, which required inventing an indicator for a specific particularly problematic anomaly, and a clever calculation of its value. Based on arXiv:2105.15167, joint with David Reutter.
Abstract: I discuss some, now quite old, applications of Wilson Operator Product Expansion in gauge theories which were developed by Valentin Zakharov, Mikhail Shifman and me.
It includes a penguin mechanism of enhancement in weak nonleptonic decays, gluon condensate and QCD sum rules, Wilsonian action in supersymmetric gauge theories and exact beta functions.
Abstract: Electron gas in 2+1D in a strong magnetic field forms fractional quantum Hall states. In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of W-infinity symmetry. As a consequence of the area-preserving diff symmetry, the electric dipole moment and the trace of quadrupole moment are conserved, which demonstrates the fractonic behavior of FQH systems. Gauging the area-preserving diff gives us a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory proposed by Pretko. Using the traceless symmetric tensor gauge formalism, I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra as well as the topological Wen-Zee term. I will extend the discussion to the area-preserving diff in 3+1D, the physical system that realizes this symmetry is skyrmions in ferromagnets.
Abstract: We construct a class of bosonic lattice Hamiltonians that exhibit fractional Hall conductivity. These Hamiltonians, while not being exactly solvable, can be reliably solved in their low energy sectors through a combination of perturbative and exact techniques. Our construction demonstrates a systematic way to circumvent the Kapustin-Fidkowski no-go theorem, and is applicable to more general cases including fermionic ones. References: Zhaoyu Han and Jing-Yuan Chen, [2107.0xxxx], Jing-Yuan Chen, [1902.06756]
Abstract: I will propose a new type of exotic quantum critical liquids, Stiefel liquids, based on 2+1 D Wess-Zumino-Witten sigma models on target space SO(N)/SO(4). The well-known deconfined quantum critical point and U(1) Dirac spin liquid are unified as two special examples of Stiefel liquids, with N=5 and N=6, respectively. Furthermore, I will argue that Stiefel liquids with N>6 are non-Lagrangian, in the sense that they cannot be described by any renormalizable continuum Lagrangian. Such non-Lagrangian states are beyond the paradigm of parton gauge mean-field theory familiar in the study of exotic quantum liquids in condensed matter physics. The intrinsic absence of any mean-field construction also means that, within the traditional approaches, it is difficult to decide whether a non-Lagrangian state can emerge from a specific UV system (such as a lattice spin system). For this purpose we hypothesize that a quantum state is emergible from a lattice system if its quantum anomalies match with the constraints from the (generalized) Lieb-Schultz-Mattis theorems. Based on this hypothesis, we find that some of the non-Lagrangian Stiefel liquids can indeed be realized in frustrated quantum spin systems, for example, on triangular or Kagome lattice, through the intertwinement between non-coplanar magnetic orders and valence-bond-solid orders. Along the way, I will also make some general comments on lattice models, renormalizable field theories and non-renormalizable field theories.
Abstract: I will introduce a family of gapped quantum phases that exhibit the phenomenology of both conventional three-dimensional topological orders and fracton orders called “Hybrid Fracton Orders”. First, I will present the simplest example of such an order: the “Hybrid X-cube” model, where excitations can be labeled identically to those of the Z2 toric code tensored with the Z2 X-cube model, but exhibit fusion and braiding properties between the two sets of excitations. Next, I will provide a general construction of hybrid fracton orders which inputs a finite group G and an abelian normal subgroup N and produces an exactly solvable model. Such order can host non-abelian fracton excitations when G is non-abelian. Furthermore, the mobilities of a general excitation is dictated by the choice of N, from which by varying, one can view as “interpolating” between a pure 3D topological order and a pure fracton order.
Abstract: Given a (2+1)D fermionic topological order and a symmetry fractionalization class for a global symmetry group G, we show how to construct a (3+1)D topologically invariant path integral for a fermionic G symmetry-protected topological state (G-FSPT) in terms of an exact combinatorial state sum. This provides a general way to compute anomalies in (2+1)D fermionic symmetry-enriched topological states of matter. Our construction uses the fermionic topological order (characterized by a super-modular tensor category) and symmetry fractionalization data to define a (3+1)D path integral for a bosonic theory that hosts a non-trivial emergent fermionic particle, and then condenses the fermion by summing over closed 3-form Z_2 background gauge fields. This procedure involves a number of non-trivial higher-form anomalies associated with Fermi statistics and fractional quantum numbers that need to be appropriately canceled off with a Grassmann integral that depends on a generalized spin structure. We show how our construction reproduces the Z_16 anomaly indicator for time-reversal symmetric topological superconductors with T^2=(−1)^F. Mathematically, with standard technical assumptions, this implies that our construction gives a combinatorial state sum on a triangulated 4-manifold that can distinguish all Z_16 Pin+ smooth bordism classes. As such, it contains the topological information encoded in the eta invariant of the pin+ Dirac operator, thus giving an example of a state sum TQFT that can distinguish exotic smooth structure.
Abstract: No definitive evidence of spacetime supersymmetry (SUSY) that transmutes fermions into bosons and vice versa has been revealed in nature so far. One may wonder whether SUSY can be realized in quantum materials. In this talk, I shall discuss how spacetime SUSY may emerge, in the sense of renormalization group flow, in the bulk of Weyl semimetals or at the boundary of topological insulators. Moreover, we have performed large-scale sign-problem-free quantum Monte Carlo simulations of various microscopic lattice models to numerically verify the emergence of spacetime SUSY at quantum critical points on the boundary of topological phases. I shall mention some experimental signatures such as optical conductivity which can be measured to test such emergent SUSY in candidate systems like the surface of 3D topological insulators. References: [1] Shao-Kai Jian, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 114, 237001 (2015) [2] Shao-Kai Jian, Chien-Hung Lin, Joseph Maciejko, and Hong Yao, Phys. Rev. Lett. 118, 166802 (2017) [3] Zi-Xiang Li, Yi-Fan Jiang, and Hong Yao, Phys. Rev. Lett. 119, 107202 (2017) [4] Zi-Xiang Li, Abolhassan Vaezi, Christian Mendl, and Hong Yao, Science Advances 4, eaau1463 (2018)
7/28/2021
Max Metlitski (MIT)
Title: Boundary criticality of the O(N) model in d = 3 critically revisited.
Abstract: It is known that the classical O(N) model in dimension d > 3 at its bulk critical point admits three boundary universality classes: the ordinary, the extra-ordinary and the special. The extraordinary fixed point corresponds to the bulk transition occurring in the presence of an ordered boundary, while the special fixed point corresponds to a boundary phase transition between the ordinary and the extra-ordinary classes. While the ordinary fixed point survives in d = 3, it is less clear what happens to the extra-ordinary and special fixed points when d = 3 and N is greater or equal to 2. I’ll show that formally treating N as a continuous parameter, there exists a critical value Nc > 2 separating two distinct regimes. For N < Nc the extra-ordinary fixed point survives in d = 3, albeit in a modified form: the long-range boundary order is lost, instead, the order parameter correlation function decays as a power of log r. For N > Nc there is no fixed point with order parameter correlations decaying slower than power law. I’ll discuss how these findings compare to recent Monte-Carlo studies of classical and quantum spin models with SO(3) symmetry. Based on arXiv:2009.05119.
Abstract: Non-Abelian phases of matter have long inspired quantum physicists across various disciplines. The strongest experimental evidence of such a phase arises in quantum Hall systems at the filling factor 5/2 but conflicts with decades of numerical works. We will briefly introduce the 5/2 plateau and explain some of the key obstacles to identifying its topological order. We will then describe recent experimental and theoretical progress, including a proposal for resolving the 5/2 enigma based on electrical conductance measurements.
8/4/2021
Nathan Benjamin (Princeton & Caltech)
Title: Harmonic analysis of 2d CFT partition functions
Abstract: I will discuss applying the theory of harmonic analysis on the fundamental domain of SL(2,Z) to partition functions of 2d conformal field theories. As an application I will decompose the partition function of c free bosons on a Narain lattice into eigenfunctions of the Laplacians of worldsheet moduli space H/SL(2,Z) and of target space moduli space O(c,c;Z)\O(c,c;R)/O(c)xO(c). This decomposition will make certain properties of Narain theories including their ensemble averages manifest. I will also discuss applying harmonic analysis to a general irrational 2d CFT and its connection with gravity in AdS3. I will prove that the primary spectrum of any 2d CFT is fully determined by a certain subset of degeneracies.
8/5/2021
Hans-Werner Hammer (TU Darmstadt)
Title: Un-nuclear physics: conformal symmetry in nuclear reactions
Abstract: I discuss a nonrelativistic version of Georgi’s “unparticle physics”. An “un-nucleus” is a field in a nonrelativistic conformal field theory characterized by a mass and a scaling dimension. It is realized approximately in high-energy nuclear reactions involving emission of a few neutrons with relative energies between about 0.1 MeV and 5 MeV. Conformal symmetry predicts a power law behavior of the inclusive cross section in this kinematic regime. I compare the predictions with previous theoretical calculations of nuclear reactions and point out opportunities to measure un-nuclei at radioactive beam facilities. Finally, I comment on the possibility to create unparticles of neutral D mesons in short-distance reactions at the LHC.
8/11/2021
Piers Coleman (Rutgers)
Title: Order Fractionalization*
Abstract: I will discuss the interplay of spin fractionalization with broken symmetry. When a spin fractionalizes into a fermion, the resulting particle can hybridize or pair with the mobile electrons to develop a new kind of fractional order parameter. The concept of “order fractionalization” enables us to extend the concept of off-diagonal order to encompass the formation of such order parameters with fractional quantum numbers, such as spinorial order[1]. A beautiful illustration of this phenomenon is provided by a model which incorporates the Yao-Lee-Kitaev model into a Kondo lattice[2]. This model explicitly exhibits order fractionalization and is expected to undergo a discrete Ising phase transition at finite temperature into an order-fractionalized phase with gapless Majorana excitations. The broader implications of these considerations for Quantum Materials and Quantum Field Theory will be discussed. * Work done in collaboration with Yashar Komijani, Anna Toth and Alexei Tsvelik. [1] Order Fractionalization, Yashar Komijani, Anna Toth, Premala Chandra, Piers Coleman, (2018). [2] Order Fractionalization in a Kitaev Kondo model, Alexei Tsvelik and Piers Coleman, (2021).
8/12/2012
Beni Yoshida (Perimeter Institute)
Title: On the firewall puzzle
Abstract: Many of the previous approaches for the firewall puzzle rely on a hypothesis that interior partner modes are embedded on the early radiation of a maximally entangled black hole. Quantum information theory, however, casts doubt on this folklore and suggests a different tale; the outgoing Hawking mode will be decoupled from the early radiation once an infalling observer, with finite positive energy, jumps into a black hole. In this talk, I will provide counterarguments against current mainstream proposals and present an alternative resolution of the firewall puzzle which is consistent with predictions from quantum information theory. My proposal builds on the fact that interior operators can be constructed in a state-independent manner once an infalling observer is explicitly included as a part of the quantum system. Hence, my approach resolves a version of the firewall puzzle for typical black hole microstates as well on an equal footing.
8/18/2021
Masaki Oshikawa (Institute for Solid State Physics, University of Tokyo)
Title: Conformal Field Theory and Modern Numerical Approach to Condensed Matter Physics Abstract: Conformal field theory (CFT) in 1+1 dimensions is a powerful framework to investigate critical phenomena. Recent developments of advanced numerical algorithms, especially tensor-network based methods, have enabled very accurate verifications of CFT predictions. They can be also combined with CFT to improve the numerical estimates. In this talk, I will review some of the applications of bulk and boundary CFT to interesting problems in condensed matter or statistical physics, and recent developments. Examples include the conduction across a junction of Tomonaga-Luttinger liquids, and an extremely precise determination of the transition temperature for the Berezinskii-Kosterlitz-Thouless transition.
8/19/2021
Ran Hong (Argonne National Laboratory) & Dominik Stoeckinger (TU Dresden)
Title: “Probing the Standard Model of Particle Physics Using the Muon Anomalous Magnetic Moment”Abstract: We present the first results of the Muon g-2 Experiment at Fermilab National Accelerator Laboratory (FNAL) and its potential theory interpretations. In the first talk the experiment method and highlights of the data analysis are presented. In the second talk the Standard Model theory prediction will be briefly explained and potential implications for physics beyond the Standard Model will be discussed. We will focus both on general aspects of model predictions as well as the current status of motivated scenarios such as the two-Higgs doublet model or the minimal supersymmetric standard model.
8/25/2021
Hitoshi Murayama (UC Berkely & IPMU)
Title: Some Exact Results in QCD-like and Chiral Gauge Theories
Abstract: I present some exact results in QCD-like chiral gauge theories. They are exact when supersymmetric gauge theories are perturbed by anomaly-mediated supersymmetry breaking (AMSB). Thanks to the UV-insensitivity of AMSB, SUSY results can be perturbed with no ambiguities even when applied to composite fields. I find two phases for QCD-like theories, one with chiral symmetry breaking and another conformal. Our results for chiral gauge theories do not agree with what had been suggested by tumbling. We suggest alternative schemes of tumbling-like interpretations. We see no evidence that large SUSY breaking leads to phase transitions at least for the chiral symmetry breaking, perhaps protected by holomorphy.
Abstract: Richard Feynman once said “Anyone who wants to analyze the properties of matter in a real problem might want to start by writing down the fundamental equations and then try to solve them mathematically. Although there are people who try to use such an approach, these people are the failures in this field. . . ”
I will summarize efforts to solve microscopic models of the cuprates using quantum Monte Carlo and density matrix renormalization group computational methods, with emphasis on how far one can get before failing to describe the real materials. I will start with an overview of the quantum chemistry of the cuprates that guides our choices of models, and then I will discuss “phases” of these models, both realized and not. I will lastly discuss the transport properties of the models in the “not-so-normal” regions of the phase diagram.
Abstract: All five-dimensional non-abelian gauge theories have a U(1) global symmetry associated with instantonic particles. I will describe a mixed ’t Hooft anomaly between this and other global symmetries such as the one-form center symmetry or the ordinary flavor symmetry for theories with fundamental matter. I will also discuss how these results can be applied to supersymmetric gauge theories in five dimensions, analyzing the symmetry enhancement patterns occurring at their conjectured RG fixed points.
Abstract: I describe a proposal for constructing lattice theories that target certain chiral gauge theories in the continuum limit. The models use reduced staggered fermions and employ site parity dependent Yukawa interactions of Fidkowski-Kitaev type to gap a subset of the lattice fermions without breaking symmetries. I show how the structure of these interactions is determined by a certain topological anomaly which is captured exactly by the generalizations of staggered fermions to triangulations of arbitrary topology. In the continuum limit the construction yields a set of sixteen Weyl fermions in agreement both with results from condensed matter physics and arguments rooted in the Dai-Freed theorem. Finally, I point out the connection to the Pati-Salam GUT model.
2/3/2020
Philip Phillips (University of Illinois Urbana-Champaign)
Abstract: High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat the electron interactions. Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity. Part of the problem is that the basic model for a Mott insulator, namely the Hubbard model is unsolvable in any dimension we really care about. To address this problem, I will start by focusing on the overlooked Z_2 emergent symmetry of a Fermi surface first noted by Anderson and Haldane. Mott insulators break this emergent symmetry. The simplest model of this type is due to Hatsugai/Kohmoto. I will argue that this model can be thought of a fixed point for Mottness. I will then show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper’s instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity. The properties of the superconducting state differ drastically from that of the standard BCS theory. The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state. Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates. [1] PWP, L. Yeo, E. Huang, Nature Physics, 16, 1175-1180 (2020).
Abstract: 4d N=1 super Yang-Mills has multiple gapped vacua arising from the spontaneously broken discrete R-symmetry. Therefore, the theory admits stable domain walls interpolating between any two vacua, but it is a nonperturbative problem to determine the low energy theory on the domain wall. We propose an explicit answer to this question: the domain walls support specific topological quantum field theories. We provide nontrivial evidence for our proposals by exactly matching renormalization group invariant partition functions (twisted by all global symmetries).
Abstract: The strange metal regime is one of the most prominent features of the cuprate phase diagram but yet has remained amongst the most mysterious. Seemingly similar metallic behavior is seen in a few other metals. In this talk, I will discuss, in great generality, some properties of `strange metals’ in an ideal clean system. I will discuss general constraints[1] on the emergent low energy symmetries of any such strange metal. These constraints may be viewed as a generalization of the Luttinger theorem of ordinary Fermi liquids. Many, if not all, non-Fermi liquids will have the same realization of emergent symmetry as a Fermi liquid (even though they could have very different dynamics). Such phases – dubbed ersatz Fermi liquids – share some (but not all) universal properties with Fermi liquids. I will discuss the implications for understanding the strange metal physics observed in experiments . Combined with a few experimental observations, I will show that these general model-independent considerations lead to concrete predictions[2] about a class of strange metals. The most striking of these is a divergent susceptibility of an observable that has the same symmetries as the loop current order parameter.
[1]. Dominic Else, Ryan Thorngren, T. Senthil, https://arxiv.org/abs/2007.0789 [2]. Dominic Else, T. Senthil, https://arxiv.org/abs/2010.10523
Abstract: Gapped phases of matter, including topological and fracton phases, are deformation classes of gapped quantum systems, and exhibit a rich array of phenomena. An interesting generalization is to consider parametrized families of gapped systems, and the deformation classes of such families. This talk will describe examples of such parametrized families and their physical properties in the bulk and at spatial boundaries. In particular, we will describe a family of one-dimensional systems that realizes a Chern number pump, which can change the quantized Chern number of a zero-dimensional family placed at its boundary.
Abstract: We will discuss an elementary way of detecting some global anomalies from the way the symmetry algebra is realized on the torus Hilbert space of the anomalous theory, give a physical description of the imprint of the “layers”that enter in the cobordism classification of anomalies and discuss applications, including how anomalies can imply a supersymmetric spectrum in strongly coupled (nonsupersymmetric) gauge theories.
Abstract: Motivated by the relation between anomaly and topological/SPT order in one higher dimension, we propose a solution to the chiral fermion problem. In particular, we find several sufficient conditions, such that a chiral fermion field theory can be regularized by an interacting lattice model in the same dimension. We also discuss some related issues, such as mass without mass term, and why ‘topological’ phase transitions are usually not “topological” phase transitions.
Abstract: Walker and I wrote down a lattice model schema to realize the (3+1)-Crane-Yetter TQFTs based on unitary pre-modular categories many years ago, and application of the model is found in a variety of places such as quantum cellular automata and fracton physics. I will start with the conceptual origin of this model as requested by the organizer. Then I will discuss a general idea for writing down lattice realizations of state-sum TQFTs based on gluing formulas of TQFTs and explain the model for Crane-Yetter TQFTs on general three manifolds. In the end, I will mention lattice models that generalize the Haah codes in two directions: general three manifolds and more than two qubits per site.
If the path integral of a quantum field theory is regarded as a generalization of the ordinary definite integral, then a lattice model of a quantum field theory could be regarded as an analogue of a Riemann sum. New lattice models in fracton physics raise an interesting question: what kinds of quantum field theories are they approximating if their continuous limits exist? Their continuous limits would be rather unusual as the local degrees of freedom of such lattice models increase under entanglement renormalization flow.
Abstract: It has long been known that there exist strings with supersymmetry on the world sheet, but not in spacetime. These include the well-known Type 0 strings, as we