Unorientable Quantum Field Theories: From crosscaps to holography
2022-10-25 09:00 - 10:30 (America/New_York) | Virtual
Quantum Matter Seminar
Speaker: João Caetano (CERN)
Title: Unorientable Quantum Field Theories: From crosscaps to holography
Abstract: In two dimensions, one can study quantum field theories on unorientable manifolds by introducing crosscaps. This defines a class of states called crosscap states which share a few similarities with the notion of boundary states. In this talk, I will show that integrable theories remain integrable in the presence of crosscaps, and this allows to exactly determine the crosscap state.

In four dimensions, the analog is to place the quantum field theory on the real projective space, the simplest unorientable 4-manifold. I will show how to do this in the example of N=4 Supersymmetric Yang-Mills, discuss its holographic description and present a new solvable setup of AdS/CFT.

Kardar-Parisi-Zhang dynamics in integrable quantum magnets
2022-11-01 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Francisco Machado (Berkeley/Harvard)
Title: Kardar-Parisi-Zhang dynamics in integrable quantum magnets
Abstract: Although the equations of motion that govern quantum mechanics are well-known, understanding the emergent macroscopic behavior that arises from a particular set of microscopic interactions remains remarkably challenging. One particularly important behavior is that of hydrodynamical transport; when a quantum system has a conserved quantity (i.e. total spin), the late-time, coarse-grained dynamics of the conserved charge is expected to follow a simple, classical hydrodynamical description. However the nature and properties of this hydrodynamical description can depend on many details of the underlying interactions. For example, the presence of additional dynamical constraints can fundamentally alter the propagation of the conserved quantity and induce slower-than-diffusion propagation. At the same time, the presence of an extensive number of conserved quantities in the form of integrability, can imbue the system with stable quasi-particles that propagate ballistically through the system.
In this talk, I will discuss another possibility that arises from the interplay of integrability and symmetry; in integrable one dimensional quantum magnets with complex symmetries, spin transport is neither ballistic nor diffusive, but rather superdiffusive. Using a novel method for the simulation of quantum dynamics (termed Density Matrix Truncation), I will present a detailed analysis of spin transport in a variety of integrable quantum magnets with various symmetries. Crucially, our analysis is not restricted to capturing the dynamical exponent of the transport dynamics and enables us to fully characterize its universality class: for all superdiffusive models, we find that transport falls under the celebrated Kardar-Parisi-Zhang (KPZ) universality class.
Finally, I will discuss how modern atomic, molecular and optical platforms provide an important bridge to connect the microscopic interactions to the resulting hydrodynamical transport dynamics. To this end, I will present recent experimental results, where this KPZ universal behavior was observed using atoms confined to an optical lattice.
[1] Universal Kardar-Parisi-Zhang dynamics in integrable quantum systems
B Ye†, FM*, J Kemp*, RB Hutson, NY Yao
(PRL in press) – arXiv:2205.02853
[2] Quantum gas microscopy of Kardar-Parisi-Zhang superdiffusion
D Wei, A Rubio-Abadal, B Ye, FM, J Kemp, K Srakaew, S Hollerith, J Rui, S Gopalakrishnan, NY Yao, I Bloch, J Zeiher
Science (2022) — arXiv:2107.00038

Topological symmetry in field theory
2022-11-08 11:30 - 13:00 | Virtual
Quantum Matter Seminar
Speaker: Daniel S. Freed (U Texas)
Title: Topological symmetry in field theory
Abstract: Recently there has been lots of activity surrounding generalized notions of symmetry in quantum field theory, including “categorical symmetries,” “higher symmetries,” “noninvertible symmetries,” etc. Inspired by definitions of abstract (finite) groups and algebras and their linear actions, we introduce a framework for these symmetries in field theory and a calculus of topological defects based on techniques in topological field theory. This is joint work with Constantin Teleman and Greg Moore.

Topology of the Fermi sea: Ordinary metals as topological materials
2022-11-15 09:30 - 11:00
Quantum Matter Seminar
Speaker: Pok Man Tam (University of Pennsylvania)
Title: Topology of the Fermi sea: Ordinary metals as topological materials
Abstract: It has long been known that the quantum ground state of a metal is characterized by an abstract manifold in momentum space called the Fermi sea. Fermi sea can be distinguished topologically in much the same way that a ball can be distinguished from a donut by counting the number of holes. The associated topological invariant, i.e. the Euler characteristic (χ_F), serves to classify metals. Here I will survey two recent proposals relating χ_F to experimental observables, namely: (i) equal-time density/number correlations [1], and (ii) Andreev state transport along a planar Josephson junction [2]. Moreover, from the perspective of quantum information, I will explain how multipartite entanglement in real space probes the Fermi sea topology in momentum space [1]. Our works not only provide a new connection between topology and entanglement in gapless quantum matters, but also suggest accessible experimental platforms to extract the topology in metals.
[1] P. M. Tam, M. Claassen, C. L. Kane, Phys. Rev. X 12, 031022 (2022)
[2] P. M. Tam and C. L. Kane, arXiv:2210.08048

3D gravity and gravitational entanglement entropy
2022-11-22 09:30 - 11:00 | Virtual
Quantum Matter Seminar
Speaker: Gabriel Wong (Harvard CMSA)
Title: 3D gravity and gravitational entanglement entropy
Abstract: Recent progress in AdS/CFT has provided a good understanding of how the bulk spacetime is encoded in the entanglement structure of the boundary CFT. However, little is known about how spacetime emerges directly from the bulk quantum theory. We address this question in an effective 3d quantum theory of pure gravity, which describes the high temperature regime of a holographic CFT. This theory can be viewed as a $q$-deformation and dimensional uplift of JT gravity. Using this model, we show that the Bekenstein-Hawking entropy of a two-sided black hole equals the bulk entanglement entropy of gravitational edge modes. These edge modes transform under a quantum group, which defines the data associated to an extended topological quantum field theory. Our calculation suggests an effective description of bulk microstates in terms of collective, anyonic degrees of freedom whose entanglement leads to the emergence of the bulk spacetime. Finally, we give a proposal for obtaining the Ryu Takayanagi formula using the same quantum group edge modes.

Symmetry in quantum field theory and quantum gravity 1
2022-12-01 10:30 - 11:30
Speaker: Daniel Harlow (MIT)
Title: Symmetry in quantum field theory and quantum gravity 1
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).

Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
2022-12-05 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Junkai Dong (Harvard University)
Title: Exact Many-Body Ground States from Decomposition of Ideal Higher Chern Bands: Applications to Chirally Twisted Graphene Multilayers
Abstract: Motivated by the higher Chern bands of twisted graphene multilayers, we consider flat bands with arbitrary Chern number C with ideal quantum geometry. While C>1 bands differ from Landau levels, we show that these bands host exact fractional Chern insulator (FCI) ground states for short range interactions. We show how to decompose ideal higher Chern bands into separate ideal bands with Chern number 1 that are intertwined through translation and rotation symmetry. The decomposed bands admit an SU(C) action that combines real space and momentum space translations. Remarkably, they also allow for analytic construction of exact many-body ground states, such as generalized quantum Hall ferromagnets and FCIs, including flavor-singlet Halperin states and Laughlin ferromagnets in the limit of short-range interactions. In this limit, the SU(C) action is promoted to a symmetry on the ground state subspace. While flavor singlet states are translation symmetric, the flavor ferromagnets correspond to translation broken states and admit charged skyrmion excitations corresponding to a spatially varying density wave pattern. We confirm our analytic predictions with numerical simulations of ideal bands of twisted chiral multilayers of graphene, and discuss consequences for experimentally accessible systems such as monolayer graphene twisted relative to a Bernal bilayer.

Neutrino Masses from Generalized Symmetry Breaking
2022-12-06 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Sungwoo Hong (U Chicago & KAIST)
Title: Neutrino Masses from Generalized Symmetry Breaking
Abstract: We explore generalized global symmetries in theories of physics beyond the Standard Model. Theories of Z′ bosons generically contain ‘non-invertible’ chiral symmetries, whose presence indicates a natural paradigm to break this symmetry by an exponentially small amount in an ultraviolet completion. For example, in models of gauged lepton family difference such as the phenomenologically well-motivated U(1)Lμ−Lτ, there is a non-invertible lepton number symmetry which protects neutrino masses. We embed these theories in gauged non-Abelian horizontal lepton symmetries, e.g. U(1)Lμ−Lτ⊂SU(3)H, where the generalized symmetries are broken nonperturbatively by the existence of lepton family magnetic monopoles. In such theories, either Majorana or Dirac neutrino masses may be generated through quantum gauge theory effects from the charged lepton Yukawas e.g. yν∼yτexp(−Sinst). These theories require no bevy of new fields nor ad hoc additional global symmetries, but are instead simple, natural, and predictive: the discovery of a lepton family Z′ at low energies will reveal the scale at which Lμ−Lτ emerges from a larger gauge symmetry.

Non-Invertible Symmetries from Holography and Branes
2022-12-12 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Federico Bonetti (Oxford)
Title: Non-Invertible Symmetries from Holography and Branes
Abstract: The notion of global symmetry in quantum field theory (QFT) has witnessed dramatic generalizations in the past few years. One of the most exciting developments has been the identification of 4d QFTs possessing non-invertible symmetries, i.e. global symmetries whose generators exhibit fusion rules that are not group-like. In this talk, I will discuss realizations of non-invertible symmetries in string theory and holography. As a concrete case study, I will consider the Klebanov-Strassler setup for holographic confinement in Type IIB string theory. The global symmetries of the holographic 4d QFT (both invertible and non-invertible) can be accessed by studying the topological couplings of the low-energy effective action of the dual 5d supergravity theory. Moreover, non-invertible symmetry defects can be realized in terms of D-branes. The D-brane picture captures non-trivial aspects of the fusion of non-invertible symmetry defects, and of their action on extended operators of the 4d QFT.

Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon
2022-12-20 09:00 - 10:30 | Virtual
Quantum Matter Seminar
Speaker: Yang Qi (Fudan)
Title: Phase Fluctuations in Two-Dimensional Superconductors and Pseudogap Phenomenon
Abstract: We study the phase fluctuations in the normal state of a general two-dimensional (2d) superconducting system with s-wave pairing. The effect of phase fluctuations of the pairing fields can be dealt with perturbatively using disorder averaging, after we treat the local superconducting order parameter as a static disordered background. It is then confirmed that the phase fluctuations above the 2d Berenzinskii-Kosterlitz-Thouless (BKT) transition give birth to the pseudogap phenomenon, leading to a significant broadening of the single-particle spectral functions. Quantitatively, the broadening of the spectral weights at the BCS gap is characterized by the ratio of the superconducting coherence length and the spatial correlation length of the superconducting pairing order parameter. Our results are tested on the attractive-U fermion Hubbard model on the square lattice, using unbiased determinant quantum Monte Carlo method and stochastic analytic continuation. We also apply our method to 2d superconductors with d-wave pairing and observe that the phase fluctuations may lead to Fermi-arc phenomenon above the BKT transition.

Reflections on Parity Breaking
2023-01-24 13:15 - 14:45 | Virtual
Quantum Matter Seminar
Speakers: Jacob McNamara (Caltech) and Matthew Reece (Harvard)
Title: Reflections on Parity Breaking
Abstract: One approach to the Strong CP Problem (known as Nelson-Barr models) is to assume that parity is a gauge symmetry, which is spontaneously broken in the world around us. In this talk, we will describe the formal meaning of parity as a gauge symmetry, and argue that the domain walls formed from spontaneous parity breaking are exactly stable. This stability can be understood as the result of an unusual sort of conserved charge, which has features in common with both gauge charges and global charges. We will explain how these charges are compatible with the expected absence of global symmetries in quantum gravity, as well as their relationship with the Swampland Cobordism Conjecture.

Group Invariant States as Many-Body Scars
2023-01-30 09:30 - 10:30 | Virtual
Quantum Matter Seminar
Title: Group Invariant States as Many-Body Scars
Speaker: Igor R. Klebanov (Princeton University)
Abstract: Quantum many-body scars have been an active area of research in Condensed Matter Physics for several years. In some many-body systems, the Hilbert space breaks up into a large ergodic sector and a much smaller scar subspace. It has been suggested [K. Pakrouski et al., Phys. Rev. Lett. 125 (2020) 230602] that the two sectors may be distinguished by their transformation properties under a large group whose rank grows with the system size (this group is not a symmetry of the Hamiltonian). The scars are invariant under this group, while all other states are not. We begin by reviewing some many-body systems where group singlet states have special properties: the matrix quantum mechanics and fermionic tensor models. We continue on to appropriately deformed versions of the SU(2) Hubbard model and show that the scar subsector is invariant under a large group, which acts on the lattice sites. More generally, we apply this idea to lattice systems with N sites that contain M Majorana fermions per site. The Hilbert space may be decomposed under the action of the SO(N)xSO(M) group, and the scars are the SO(N) singlets. For any even M, there are two families of scars. One of them, which we call the eta-states, is symmetric under the group O(N) that includes a reflection. The other, the zeta-states, has the SO(N) invariance only. For M=4, where our construction reduces to a deformed SU(2) Hubbard chain with local interactions, the former family are the N+1 eta-pairing states, while the latter are the N+1 states of maximum spin. For M=6, we exhibit explicit formulae for the scar states and calculate the bipartite entanglement entropy analytically. For large N, it grows logarithmically with the region size. In general, the energies of the scars within each family are not equidistant. For M>6 we also find that, with local Hamiltonians, the scars typically have certain degeneracies. The latter part of the talk is based on the recent paper “Majorana Scars as Group Singlets” by Zimo Sun, Fedor Popov, Igor Klebanov and Kiryl Pakrouski, arXiv:2212.11914

Fracton orders in hyperbolic space and its excitations with fractal mobility
2023-02-03 10:30 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Han Yan (Rice U)
Title: Fracton orders in hyperbolic space and its excitations with fractal mobility
Abstract: Unlike ordinary topological quantum phases, fracton orders are intimately dependent on the underlying lattice geometry. In this work, we study a generalization of the X-cube model, on lattices embedded in a stack of hyperbolic planes. We demonstrate that for certain hyperbolic lattice tesselations, this model hosts a new kind of subdimensional particle, treeons, which can only move on a fractal-shaped subset of the lattice. Such an excitation only appears on hyperbolic geometries; on flat spaces, treeons become either a lineon or a planeon. Additionally, we find intriguingly that for certain hyperbolic tessellations, a fracton can be created by a membrane operator (as in the X-cube model) or by a fractal-shaped operator within the hyperbolic plane. Our work shows that there are still plenty of exotic behaviors from fracton order to be explored, especially when the embedding geometry is curved.
Reference: H. Yan, K. Slage, A. H. Nevidomskyy, arXiv:2211.15829

Non-invertible Symmetry Enforced Gaplessness
2023-02-10 10:30 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Ho Tat Lam (MIT)
Title: Non-invertible Symmetry Enforced Gaplessness
Abstract: Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain infrared dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum, leaving only two possibilities for the infrared dynamics: a gapless state or spontaneous breaking of the non-invertible symmetries. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics
2023-02-17 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Rahul Sahay (Harvard)
Title: Quantum Spin Lakes: NISQ-Era Spin Liquids from Non-Equilibrium Dynamics
Abstract: While many-body quantum systems can in principle host exotic quantum spin liquid (QSL) states, realizing them as ground states in experiments can be prohibitively difficult. In this talk, we show how non-equilibrium dynamics can provide a streamlined route toward creating QSLs. In particular, we show how a simple Hamiltonian parameter sweep can dynamically project out condensed anyons from a family of initial product states (e.g. dynamically “un-Higgs”), yielding a QSL-like state. We christen such states “quantum spin lakes” which, while not thermodynamically large QSLs, enable their study in NISQ-era quantum simulators. Indeed, we show that this mechanism sheds light on recent experimental and numerical observations of the dynamical state preparation of the ruby lattice spin liquid in Rydberg atom arrays. Time permitting, we will discuss how our theory motivates a tree tensor network-based numerical tool—reliant on our theory—that quantitatively reproduces the experimental data two orders of magnitude faster than conventional brute-force simulation methods. Finally, we will highlight that even spin liquid states that are unstable in equilibrium—namely, 2 + 1D U(1) spin liquid states—can be robustly prepared by non-equilibrium dynamics.

Strongly coupled ultraviolet fixed point and symmetric mass generation in four dimensions with 8 Kähler-Dirac fermions
2023-03-03 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Anna Hasenfratz (University of Colorado)
Title: Strongly coupled ultraviolet fixed point and symmetric mass generation in four dimensions with 8 Kähler-Dirac fermions

Abstract: 4-dimensional gauge-fermion systems exhibit a quantum phase transition from a confining, chirally broken phase to a conformal phase as the number of fermions is increased. While the existence of the conformal phase is well established, very little is known about the nature of the phase transition or the strong coupling phase.

Lattice QCD methods can predict the RG $beta$ function, but the calculations are often limited by non-physical bulk phase transition that prevent exploring the strong coupling region of the phase diagram. Even the critical flavor number is controversial, estimates vary between $N_f=8$ and 14 for fundamental fermions.

Using an improved lattice actions that include heavy Pauli-Villars (PV) type bosons to reduce ultraviolet fluctuations, I was able to simulate an SU(3) system with 8 fundamental flavors at much stronger renormalized coupling than previously possibly. The numerical results indicate a smooth phase transition from weak coupling to a strongly coupled phase.
I investigate the critical behavior of the transition using finite size scaling. The result of the scaling analysis is not consistent with a first order phase transition, but it is well described by Berezinsky-Kosterlitz-Thouless or BKT scaling. BKT scaling could imply that the 8-flavor system is the opening of the conformal window, an exciting possibility that warrants further investigations.

The strongly coupled phase appear to be chirally symmetric but gapped, suggesting symmetric mass generation (SMG). This could be the consequence of the lattice fermions used in this study. Staggered fermions in the massless limit are known to be anomaly free, allowing an SMG phase in the continuum limit.

References:
Phys.Rev.D 106 (2022) 1, 014513 • e-Print: 2204.04801
Phys.Rev.D 104 (2021) 7, 074509 • e-Print: 2109.02790
For anomalies and staggered fermion, see
Phys.Rev.D 104 (2021) 9, 094504 • e-Print: 2101.01026

https://www.youtube.com/watch?v=3jtNsFGszjE&list=PL0NRmB0fnLJQAnYwkpt9PN2PBKx4rvdup&index=14

Quantum entropy thermalization
2023-03-10 10:00 - 11:00 | Virtual
Quantum Matter Seminar
Speaker: Yichen Huang (Harvard)
Title: Quantum entropy thermalization
Abstract: In an isolated quantum many-body system undergoing unitary evolution, the entropy of a subsystem (smaller than half the system size) thermalizes if at long times, it is to leading order equal to the thermodynamic entropy of the subsystem at the same energy. We prove entropy thermalization for a nearly integrable Sachdev-Ye-Kitaev model initialized in a pure product state. The model is obtained by adding random all-to-all 4-body interactions as a perturbation to a random free-fermion model. In this model, there is a regime of “thermalization without eigenstate thermalization.” Thus, the eigenstate thermalization hypothesis is not a necessary condition for thermalization.
References: arXiv:2302.10165, 2209.09826; Joint work with Aram W. Harrow

Tensorial TQFT and disentangling modular Walker-Wang models
2023-03-17 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Andreas Bauer (Freie Universität Berlin)
Title: Tensorial TQFT and disentangling modular Walker-Wang models
Abstract: I will introduce simple “tensorial” definitions for many algebraic and categorical structures appearing in the classification of topological phases of matter. Such “tensorial TQFTs” will be defined as maps that associate tensors to geometric/topological objects of some type, subject to gluing axioms. Tensorial TQFTs are very directly related to microscopic physical models in terms of discrete path integrals. I will use those tensorial definitions to construct invertible boundaries which disentangle modular Walker-Wang models.

Traversable wormhole dynamics on a quantum processor
2023-03-24 10:00 - 11:30 | Hybrid – G10
Quantum Matter Seminar
Speaker: Alexander Zlokapa, MIT
Title: Traversable wormhole dynamics on a quantum processor
Abstract: The holographic principle, theorized to be a property of quantum gravity, postulates that the description of a volume of space can be encoded on a lower-dimensional boundary. The anti-de Sitter (AdS)/conformal field theory correspondence or duality is the principal example of holography. The Sachdev–Ye–Kitaev (SYK) model of N >> 1 Majorana fermions has features suggesting the existence of a gravitational dual in AdS2, and is a new realization of holography. We invoke the holographic correspondence of the SYK many-body system and gravity to probe the conjectured ER=EPR relation between entanglement and spacetime geometry through the traversable wormhole mechanism as implemented in the SYK model. A qubit can be used to probe the SYK traversable wormhole dynamics through the corresponding teleportation protocol. This can be realized as a quantum circuit, equivalent to the gravitational picture in the semiclassical limit of an infinite number of qubits. Here we use learning techniques to construct a sparsified SYK model that we experimentally realize with 164 two-qubit gates on a nine-qubit circuit and observe the corresponding traversable wormhole dynamics. Despite its approximate nature, the sparsified SYK model preserves key properties of the traversable wormhole physics: perfect size winding, coupling on either side of the wormhole that is consistent with a negative energy shockwave, a Shapiro time delay, causal time-order of signals emerging from the wormhole, and scrambling and thermalization dynamics. Our experiment was run on the Google Sycamore processor. By interrogating a two-dimensional gravity dual system, our work represents a step towards a program for studying quantum gravity in the laboratory. Future developments will require improved hardware scalability and performance as well as theoretical developments including higher-dimensional quantum gravity duals and other SYK-like models.

Enhancing Detection of Topological Order by Local Error Correction
2023-04-07 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Nishad Maskara (Harvard)
Title: Enhancing Detection of Topological Order by Local Error Correction
Abstract: The exploration of topologically-ordered states of matter is a long-standing goal at the interface of several subfields of the physical sciences. Such states feature intriguing physical properties such as long-range entanglement, emergent gauge fields and non-local correlations, and can aid in realization of scalable fault-tolerant quantum computation. However, these same features also make creation, detection, and characterization of topologically-ordered states particularly challenging. Motivated by recent experimental demonstrations, we introduce a new paradigm for quantifying topological states—locally error-corrected decoration (LED)—by combining methods of error correction with ideas of renormalization-group flow. Our approach allows for efficient and robust identification of topological order, and is applicable in the presence of incoherent noise sources, making it particularly suitable for realistic experiments. We demonstrate the power of LED using numerical simulations of the toric code under a variety of perturbations, and we subsequently apply it to an experimental realization of a quantum spin liquid using a Rydberg-atom quantum simulator. Finally, we illustrate how LED can be applied to more general phases including non-abelian topological orders.

Fault-tolerant quantum computation via topological order on fractals and emergent symmetries
2023-04-14 10:00 - 11:30 | Hybrid – G10
Quantum Matter Seminar
Speaker: Guanyu Zhu (IBM Quantum, T. J. Watson Research Center)
Title: Fault-tolerant quantum computation via topological order on fractals and emergent symmetries
Abstract: Topological quantum error correcting codes in integer spatial dimensions have been widely studied in the field of quantum information. A remaining major challenge is to reduce the space-time overhead for universal fault-tolerant quantum computation with topological codes. In the first part of my talk, I will present a theory of topological order and quantum codes on fractals embedded in three and higher dimensions and its connection to systolic geometry. The construction of such fractal codes can hence significantly reduce the space overhead. In the second part, I will show how to perform fault-tolerant non-Clifford logical gates in such fractal codes using the idea of emergent symmetries. In particular, I will discuss the existence of higher-form symmetries corresponding to sweeping of certain codimension-2 invertible defects and exotic gapped boundaries which condense such defects.
References:
1. PRX Quantum 3 (3), 030338 (2022), Guanyu Zhu, Tomas Jochym-O’Connor, Arpit Dua
2. arXiv:2201.03568 (2022), Arpit Dua, Tomas Jochym-O'Connor, Guanyu Zhu
3. arXiv:2208.07367 (2022), Maissam Barkeshli, Yu-An Chen, Sheng-Jie Huang, Ryohei Kobayashi, Nathanan Tantivasadakarn, Guanyu Zhu

A model of the cuprates: from the pseudogap metal to d-wave superconductivity and charge order
2023-04-21 10:00 - 11:30 | Hybrid – G10
Quantum Matter Seminar
Speaker: Prof. Subir Sachdev (Harvard)
Title: A model of the cuprates: from the pseudogap metal to d-wave superconductivity and charge order
Abstract: Soon after the discovery of high-temperature superconductivity in the cuprates, Anderson proposed a connection to quantum spin liquids. But observations since then have shown that the low-temperature phase diagram is dominated by conventional states, with a competition between superconductivity and charge-ordered states which break translational symmetry. We employ the “pseudogap metal” phase, found at intermediate temperatures and low hole doping, as the parent to the phases found at lower temperatures. The pseudogap metal is described as a fractionalized phase of a single-band model, with small pocket Fermi surfaces of electron-like quasiparticles whose enclosed area is not equal to the free electron value, and an underlying pi-flux spin liquid with an emergent SU(2) gauge field. This pi-flux spin liquid is now known to be unstable to confinement at sufficiently low energies. We develop a theory of the different routes to confinement of the pi-flux spin liquid and show that d-wave superconductivity, antiferromagnetism, and charge order are natural outcomes. We argue that this theory provides routes to resolving a number of open puzzles on the cuprate phase diagram.
As a side result, at half-filling, we propose a deconfined quantum critical point between an antiferromagnet and a d-wave superconductor described by a conformal gauge theory of 2 flavors of massless Dirac fermions and 2 flavors of complex scalars coupled as fundamentals to a SU(2) gauge field.
This talk is based on Maine Christos, Zhu-Xi Luo, Henry Shackleton, Mathias S. Scheurer, and S. S., arXiv:2302.07885

Fracton Self-Statistics
2023-04-28 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Title: Fracton Self-Statistics
Speaker: Hao Song (ITP-CAS)
Abstract: Fracton order describes novel quantum phases of matter that host quasiparticles with restricted mobility, and thus lies beyond the existing paradigm of topological order. In particular, excitations that cannot move without creating other excitations are called fractons. Here we address a fundamental open question — can the notion of self-exchange statistics be naturally defined for fractons, given their complete immobility as isolated excitations? Surprisingly, we demonstrate how fractons can be exchanged, and show their self-statistics is a key part of the characterization of fracton orders. We derive general constraints satisfied by the fracton self-statistics in a large class of abelian fracton orders. Finally, we show the existence of semionic or fermionic fracton self-statistics in some twisted variants of the checkerboard model and Haah’s code, establishing that these models are in distinct quantum phases as compared to their untwisted cousins.
References: H Song, N Tantivasadakarn, W Shirley, M Hermele, arXiv:2304.00028.

Detecting central charge in a superconducting quantum processor
2023-05-05 10:00 - 11:30 | Hybrid – G10
Quantum Matter Seminar
Speaker: Sona Najafi (IBM Quantum)
Title: Detecting central charge in a superconducting quantum processor
Abstract: Physical systems at the continuous phase transition point exhibit conformal symmetry rendering local scaling invariance. In two dimensions, the conformal group possesses infinite generators described by Virasoro algebra with an essential parameter known as a central charge. While the central charge manifests itself in a variety of quantities, its detection in experimental setup remains elusive. In this work, we utilize Shannon-Renyi entropy on a local basis of a one-dimensional quantum spin chain at a critical point. We first use a simulated variational quantum eigen solver to prepare the ground state of the critical transfer field Ising model and XXZ model with open and periodic boundary conditions and perform local Pauli X and Z basis measurements. Using error mitigation such as probabilistic error cancellation, we extract an estimation of the local Pauli observables needed to determine the Shannon-Renyi entropy with respect to subsystem size. Finally, we obtain the central charge in the sub-leading term of Shannon-Renyi entropy.

Anomalies of (1+1)D categorical symmetries
2023-05-12 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Carolyn Zhang (U Chicago)
Title: Anomalies of (1+1)D categorical symmetries
Abstract: We present a general approach for detecting when a fusion category symmetry is anomalous, based on the existence of a special kind of Lagrangian algebra of the corresponding Drinfeld center. The Drinfeld center of a fusion category $A$ describes a $(2+1)D$ topological order whose gapped boundaries enumerate all $(1+1)D$ gapped phases with the fusion category symmetry, which may be spontaneously broken. There always exists a gapped boundary, given by the emph{electric} Lagrangian algebra, that describes a phase with $A$ fully spontaneously broken. The symmetry defects of this boundary can be identified with the objects in $A$. We observe that if there exists a different gapped boundary, given by a emph{magnetic} Lagrangian algebra, then there exists a gapped phase where $A$ is not spontaneously broken at all, which means that $A$ is not anomalous. In certain cases, we show that requiring the existence of such a magnetic Lagrangian algebra leads to highly computable obstructions to $A$ being anomaly-free. As an application, we consider the Drinfeld centers of $mathbb{Z}_Ntimesmathbb{Z}_N$ Tambara-Yamagami fusion categories and recover known results from the study of fiber functors.

Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24
2023-06-09 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speakers: Gerald Höhn (Kansas State University) & Sven Möller (University of Hamburg)
Title: Classification of Self-Dual Vertex Operator Superalgebras of Central Charge at Most 24
Abstract: We discuss the classfication of self-dual vertex operator superalgebras (SVOAs) of central charge 24, or in physics parlance the purely chiral 2-dimensional fermionic conformal field theories with just one primary field.
There are exactly 969 such SVOAs under suitable regularity assumptions and the assumption that the shorter moonshine module VB^# is the unique self-dual SVOA of central charge 23.5 whose weight-1/2 and weight-1 spaces vanish.
We construct and classify the self-dual SVOAs by determining the 2-neighbourhood graph of the self-dual (purely bosonic) VOAs of central charge 24 and also by realising them as simple-current extensions of a dual pair containing a certain maximal lattice VOA. We show that all SVOAs besides VB^# x F and potential fake copies thereof stem from elements of the Conway group Co_0, the automorphism group of the Leech lattice.
By splitting off free fermions F, if possible, we obtain the classification for all central charges less than or equal to 24.
Reference: G. Höhn, S. Möller, arXiv:2303.17190.

Small Bosonic CFTs, Chiral Fermionization, and Symmetry/Subalgebra Duality
2023-06-13 10:00 - 12:00 | Virtual
Quantum Matter Seminar
Speaker: Brandon C. Rayhaun (C. N. Yang ITP, Stony Brook University)
Title: Small Bosonic CFTs, Chiral Fermionization, and Symmetry/Subalgebra Duality
Abstract: Conformal field theories in (1+1)D are key actors in many dramas of physics and mathematics. Their classification has therefore been an important and long-standing problem. In this talk, I will explain the main ideas behind the classification of (most) “small” bosonic CFTs. Here, I use the adjective “small” informally to refer to theories with low central charge (less than 24) and few primary operators (less than 5). Time and attention permitting, I will highlight two applications of this result. First, I will describe how it can be used in tandem with bosonization and fermionization techniques to establish the classification of chiral fermionic CFTs with central charge less than 23. Second, I will showcase how it can be used to bootstrap generalized global symmetries using the concept of “symmetry/subalgebra duality.”
Talk based on arXiv:2208.05486 [hep-th] (joint work with Sunil Mukhi) and arXiv:2303.16921 [hep-th].

Chiral fermionic CFTs of central charge ≤ 16
2023-06-26 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Title: Chiral fermionic CFTs of central charge ≤ 16
Abstract: We classified all chiral fermionic CFTs of central charge ≤ 16 using Kac’s theorem and bosonization/fermionization. This talk will discuss the derivation of this result, its application to the classification of non-supersymmetric heterotic string theories, and along the way we’ll address some oft-overlooked subtleties of bosonization from the point of view of anomalies and topological phases.

Monopoles, Scattering, and Generalized Symmetries
2023-06-30 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Marieke Van Beest (SCGP)
Title: Monopoles, Scattering, and Generalized Symmetries
Abstract: In this talk, we will discuss the problem of electrically charged, massless fermions scattering off magnetic monopoles. The interpretation of the outgoing states has long been a puzzle, as they can carry fractional quantum numbers. We argue that such outgoing particles live in the twisted sector of a topological co-dimension 1 surface, which ends topologically on the monopole. This symmetry defect is often non-invertible, and as such the outgoing radiation not only carries unconventional flavor quantum numbers, but is often trailed by a topological field theory, which is a new prediction.

Two of my favorite numbers: 8 and 24
2023-08-24 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: John Baez (University of California, Riverside)
Title: Two of my favorite numbers: 8 and 24
Abstract: The numbers 8 and 24 play special roles in mathematics. The number 8 is special because of Bott periodicity, the octonions and the E8 lattice, while 24 is special for many reasons, including the binary tetrahedral group, the 3rd stable homotopy group of spheres, and the Leech lattice. The number 8 does for superstring theory what the number 24 does for bosonic string theory. In this talk, which is intended to be entertaining, I will overview these matters and also some connections between the numbers 8 and 24.
