Previous Quantum Matter/Condensed Matter Seminars

Spring 2020:

2/5/2020Ya-Hui Zhang (Harvard)


Title: A new theory for pseudogap metal in hole doped cuprates

Abstract: We provide a new parton theory for hole doped cuprates. We will describe both a pseudogap metal with small Fermi surfaces and the conventional Fermi liquid with large Fermi surfaces within mean field level of the same framework. For the pseudogap metal, “Fermi arc” observed in ARPES can be naturally reproduced. We also provide a theory for a critical point across which the carrier density jumps from x to 1+x. We will also discuss the generalization of the theory to Kondo breaking down transition in heavy fermion systems and generic SU(N) Hubbard model.

2/6/2020Yuan Cao (MIT)Title: Twistronics in Graphene Superlattices: Correlation and Superconductivity
2/12/2020Xue-Yang Song (Harvard)


Title: Monopoles in QED3 Dirac Spin Liquids
2/13/2020Grigory Tarnopolskiy (Harvard)


Title: Spontaneous symmetry breaking in SYK models
2/19/2020Zhehao Dai (MIT)



Title: Modeling the pseudogap state in cuprates: quantum disordered pair density wave

Abstract: I will briefly review the pseudogap phenomenology in high Tc cuprate superconductors, especially recent experiments related to charge density waves and pair density waves, and propose a simple theory of the pseudogap. By quantum disordering a pair density wave, we found a state composed of insulating antinodal pairs and a nodal electron pocket. We compare the theoretical predictions with ARPES results, optical conductivity, quantum oscillation and other experiments.

2/20/2020Lokman Tsui (MIT)


Title: Lattice models that realize $Z_n$ 1-symmetry-protected topological states for even $n$

Abstract: Higher symmetries can emerge at low energies in a topologically ordered state with no symmetry, when some topological excitations have very high energy scales while other topological excitations have low energies. The low energy properties of topological orders in this limit, with the emergent higher symmetries, may be described by higher symmetry protected topological order. This motivates us, as a simplest example, to study a lattice model of $Z_n$-1-symmetry protected topological (1-SPT) states in 3+1D for even $n$. We write down an exactly solvable lattice model and study its boundary transformation. On the boundary, we show the existence of anyons with non-trivial self-statistics. For the $n=2$ case, where the bulk classification is given by an integer $m$ mod 4, we show that the boundary can be gapped with double semion topological order for $m=1$ and toric code for $m=2$. The bulk ground state wavefunction amplitude is given in terms of the linking numbers of loops in the dual lattice. Our construction can be generalized to arbitrary 1-SPT protected by finite unitary symmetry.



Wei Zhang (MIT)


Title: “Cohomology of Shimura Variety”
2/27/2020Nat Tantivasadakarn (Harvard)


Title: Jordan-Wigner Dualities for translation-invariant Hamiltonians in any dimension

Abstract: Inspired by recent constructions of Jordan-Wigner transformations in higher dimensions by Kapustin et. al., I will present a framework for an exact bosonization, which locally maps a translation-invariant model of spinless fermions to gauge theory of Pauli spins. I will show that the duality exists for an arbitrary number of (possibly many-body) “hopping” operators in any dimension and provide an explicit construction. The duality can be concisely stated in terms of an algebraic formalism of translation-invariant Hamiltonians proposed by Haah.  I will then present two interesting applications. First, bosonizing Majorana stabilizer codes, such as the Majorana color code or the checkerboard model, into Pauli stabilizer codes. Second, bosonizing fermionic systems where fermion parity is conserved on submanifolds such as higher-form, line, planar or fractal symmetry. In 3+1D, the latter two can give rise to fracton models where emergent particles are immobile, but yet can be “fermionic”. This may give rise to new non-relativistic ‘t Hooft anomalies.



Robert Gompf (UT Austin)


Title: Cutting and pasting 4-manifolds

Abstract: We will discuss techniques topologists use for understanding 4-manifolds obtained by cut-and-paste constructions. The hope is that these techniques may be useful for understanding 4-dimensional topological field theories.
3/11/2020Zhengwei Liu (Harvard) 


Title: Quantized Graphs and Quantum Error Correction

Abstract: Graph theory is important in information theory. We introduce a quantization process on graphs and apply the quantized graphs in quantum information. The quon language provides a mathematical theory to study such quantized graphs in a general framework. We give a new method to construct graphical quantum error correcting codes on quantized graphs and characterize all optimal ones. We establish a further connection to geometric group theory and construct quantum low-density parity-check stabilizer codes on the Cayley graphs of groups. Their logical qubits can be encoded by the ground states of newly constructed exactly solvable models with translation-invariant local Hamiltonians. Moreover, the Hamiltonian is gapped in the large limit when the underlying group is infinite.
3/12/2020 Cancelled 
3/18/2020Spring Break 
3/19/2020Spring Break  
3/25/2020Zhehao Dai (MIT) 


Title: Fluctuating pair density wave in cuprates

Abstract: Recent high-field low-temperature data shed new light on the mysterious pseudogap phase in cuprates. I will introduce a simple way to synthesize the low-temperature data, the charge density wave, and the previous ARPES and optical data. In the meantime, I will discuss the general problem of how fluctuating superconducting order changes the fermion spectrum and other response functions.
3/26/2020Juven Wang (Harvard CMSA)Title: A Dynamical Model for Virus Spreading in Populations

Abstract: We propose a set of dynamical non-linear governing differential equations to analyze the virus spreading in a population, with the aim towards applications for the COVID-19. We consider (I) a non-growing closed system, (II) a growing closed system, and (III) a growing open system. Possible sources of dynamical data can be found online.
4/1/2020Jong Yeon Lee (Harvard)  


This meeting will be taking place virtually on Zoom.

Title: Exploration on Deconfined Fractionalized Particles at Quantum Criticality — Fractional Chern Insulators and Shastry-Sutherland Quantum Magnets

Abstract: One of the most exotic phenomena in condensed matter systems is the emergence of fractionalized particles. However, until now, only a few experimental systems are known to realize fractionalized excitations. This calls for more systematic ways to find and understand systems with fractionalization. One natural starting point is to look for an exotic quantum criticality, where the fundamental degrees of freedom become insufficient to describe the system accurately. Furthermore, understandings in exotic quantum critical phenomena would provide a unified perspective on nearby gapped phases, i.e. a guiding principle to engineer the system in a desirable direction that may host anyons. In this talk, I would present my works on two different types of quantum criticality: (1) Deconfined quantum critical point (DQCP) between plaquette valence-bond solids and Neel ordered state in Shastry-Sutherland lattice models [PRX 9, 041037 (2019)], where two distinct symmetry breaking order parameters become unified by the fractionalized degree of freedom. (2) Transitions between fractional Chern/Quantum Hall insulators tuned by the strength of lattice potential [PRX 8, 031015 (2018)]. Here, the low-lying excitations are already fractionalized; therefore, the deconfined fractional excitations follows more naturally, which is described by Chern-Simons quantum electrodynamics. The numerical results using iDMRG as well as theoretical analysis of their emergent critical properties would be presented. In the end, I would discuss their spectroscopic signatures, providing a full analysis of experimental verification.

4/2/2020Zheyan Wan (YMSC, Tsinghua University) This meeting will be taking place virtually on Zoom.

Title: Computation of cobordism groups with applications in physics

Abstract: By the generalized Pontryagin-Thom isomorphism, cobordism groups are the homotopy groups of certain spectra. Adams spectral sequence is a powerful tool to compute homotopy groups of spectra. In this first talk, I will introduce some basic notions and tools involved in the computation of cobordism groups. This talk is based on,,, jointly with Juven Wang and Yunqin Zheng.

4/8/2020Chang-Tse Hsieh (IPMU and U Tokyo)  

This meeting will be taking place virtually on Zoom.

Title: Anomaly of the Electromagnetic Duality of Maxwell Theory

Abstract: Every physicist knows that the classical electromagnetism is described by Maxwell’s equations and that it is invariant under the electromagnetic duality S: (E, B) → (B, −E). However, the properties of the electromagnetic duality in the quantum theory might not be as well known to physicists in general, and in fact are not very well understood in the literature. This is particularly true when going around a nontrivial path in the spacetime results in a duality transformation. In our recent work, we uncovered a feature of the Maxwell theory and its duality symmetry in such a situation, namely that it has a quantum anomaly. We found that the anomaly of this system in a particular formulation is 56 times that of a Weyl fermion. Our result reproduces, as a special case, the known anomaly of the all-fermion electrodynamics—a version of the Maxwell theory where particles of odd (electric or magnetic) charge are fermions—discovered in the last few years.

5:00 – 6:00pm
Juven Wang (Harvard CMSA)This meeting will be taking place virtually on Zoom.

Title: Quantum Matter Adventure to Fundamental Physics and Mathematics

Abstract: In 1956, T. D. Lee and C. N. Yang questioned the Parity Conservation in Weak Interactions in particle physics. In less than one year, experimentalists confirmed the weak interactions are indeed maximally parity-violating. The parity violation by chiral fermions now is a Standard Model physics textbook statement, but it goes without any down-to-earth explanation for long. Why? We will see how the recent physics development in Quantum Matter may guide us to give an adventurous story and possibly a new elementary explanation.  We will see how the topology and cobordism in mathematics may come into the play of anomalies and non-perturbative interactions in fundamental physics. We propose that Spin(10) chiral fermion theories with Weyl fermions in 16-dimensional spinor representations can be defined non-perturbatively (such as on a 3+1D lattice), and subsequently dynamically gauged to be a Spin(10) chiral gauge theory for SO(10) Grand Unification, without fermion doubling. Perhaps some of you (geometers, string theorists, etc.) can team up with me to understand the “boundary conditions” of the Standard Model and Beyond.

Work-based on and Refs therein: arXiv:1809.11171, 1810.00844, 1812.11967, and 1910.14668.
4/9/2020 Zheyan Wan (YMSC, Tsinghua University)This meeting will be taking place virtually on Zoom.

 Title: Computation of cobordism groups with applications in physics 2

Abstract: Following the first talk, I will illustrate how to use Adams spectral sequence. Using Adams spectral sequence, I will compute some Spin, Spin^c, Spin^h cobordism groups. This talk is based on,,, jointly with Juven Wang and Yunqin Zheng.

4/15/2020Tian Lan (University of Waterloo, Canada)

This meeting will be taking place virtually on Zoom.

Title: Introduction to Categorical Approach to Topological Phases in Arbitrary Dimensions

Abstract: I will talk about some ideas that are essential to build a general framework for topological phases in arbitrary dimensions. I will also discuss how these ideas are applied when global symmetry or higher symmetry is present, and how to understand and classify such higher SET/SPT orders.
4/16/2020Marius Lemm (Harvard) 

This meeting will be taking place virtually on Zoom.  

Abstract: Quantum spin systems are many-body models which are of wide interest in modern physics and at the same time amenable to rigorous mathematical analysis. A central question about a quantum spin system is whether its Hamiltonian exhibits a spectral gap above the ground state. The existence of such a spectral gap has far-reaching consequences, e.g., for the ground state complexity. In this talk, we survey recent progress regarding spectral gaps for frustration-free quantum spin systems in dimensions greater than 1 such as the antiferromagnetic models of Affleck-Kennedy-Lieb-Tasaki (AKLT).

4/22/2020Joe Davighi (University of Cambridge)

This meeting will be taking place virtually on Zoom.

Title: Global anomalies in the Standard Model(s) and Beyond

Abstract: Global anomalies in gauge theories are detected by the exponentiated eta-invariant, which becomes a cobordism invariant when perturbative anomalies vanish. We analyse global anomalies in four distinct (but equally valid) versions of the Standard Model of particle physics by computing the appropriate cobordism groups. In two cases we find that there are no global anomalies beyond the Witten anomaly associated with the SU(2) factor, while in the other cases we show that there are no global anomalies at all. This uncovers a subtle interplay between local and global anomalies in closely related gauge theories. We will then discuss a more subtle version of this `anomaly interplay’ occurring in a U(2) gauge theory defined without a spin structure.

4/23/2020Haoyu Guo (Harvard)

This meeting will be taking place virtually on Zoom.

Title: Linear in temperature resistivity in the limit of zero temperature from the time reparameterization soft mode

Abstract: The most puzzling aspect of the `strange metal’ behavior of correlated electron compounds is that the linear in temperature resistivity often extends down to low temperatures, lower than natural microscopic energy scales. We consider recently proposed deconfined critical points (or phases) in models of electrons in large dimension lattices with random nearest-neighbor exchange interactions. The criticality is in the class of Sachdev-Ye-Kitaev models, and exhibits a time reparameterization soft mode representing quantum gravity in dual holographic theories. We compute the low temperature resistivity in a large $M$ limit of models with SU($M$) spin symmetry, and find that the dominant temperature dependence arises from this soft mode. The resistivity is

linear in temperature down to zero temperature at the critical point, with a
co-efficient universally proportional to the product of the residual resistivity and the co-efficient of the linear in temperature specific heat. We argue that the time reparameterization soft mode offers a promising and generic mechanism for resolving the strange metal puzzle.

Nakarin Lohitsiri  (Univeristy of Cambridge)

This meeting will be taking place virtually on Zoom.

Title: If the Weak Were Strong and the Strong Were Weak

Abstract: I will give an account of the work ArXiv:1907.08221 where we explore the phase structure of the Standard Model as the relative strengths of the SU(2) weak force and SU(3) strong force are varied. With a single generation of fermions, the structure of chiral symmetry breaking suggests that there is no phase transition as we interpolate between the SU(3)-confining phase and the SU(2) confining phase. Remarkably, the massless left-handed neutrino, familiar in our world, morphs smoothly into a massless right-handed down-quark. With multiple generations, a similar metamorphosis occurs, but now proceeding via a phase transition.

4/30/2020Zohar Komargodski (Stony Brook)

This meeting will be taking place virtually on Zoom.

Abstract: A natural conjecture is that at high enough temperatures, due to thermal fluctuations, order must be restored. We examine this conjecture by studying some concrete Quantum Field Theories.
We find some counter-examples and discuss their properties.
5/6/2020Erich Poppitz (University of Toronto)

This meeting will be taking place virtually on Zoom.

Title: Domain walls, anomalies, and deconfinement

Abstract: “Generalized” ’t Hooft anomalies impose new constraints on nonperturbative gauge dynamics. In confining theories with domain walls, they imply that quarks become liberated on the walls. The pertinent anomaly-inflow arguments have a formal flavor and our goal here is to shed light on dynamical aspects of domain-wall deconfinement. We use semiclassical means in a theoretically controlled setting. While these tools do not require supersymmetry, for brevity (and elegance) we focus this talk on 4d N=1 super Yang-Mills theory. We review the set-up and study the domain walls’ properties, along the way deriving the “N choose k” multiplicity of k-walls (connecting vacua k steps” apart). We use the results to explain how quarks of all N-alities become deconfined on all k-walls. A similar picture applies to deconfinement on domain walls in QCD at theta=pi, adjoint QCD, and axion domain walls. We end with discussing a wish list” of not well-understood aspects. (The bulk of this talk is based on 1909.10979, with Cox and Wong. However, it relies heavily on 1501.06773, with Anber and Sulejmanpasic, as well as 2001.03631, with Anber.)
5/7/2020Sahand Seifnashri (SUNY) 

This meeting will be taking place virtually on Zoom.

Title: Line Operators of Gauge Theories on Non-Spin Manifolds

Abstract: I will talk about line operators of four-dimensional gauge theories on non-spin manifolds. Line operators correspond to worldlines of heavy classical particles. Specifying the spectrum of such particles/lines, leads to distinct physical theories with different discrete theta parameters. We propose a formula for the spin of line operators (boson or fermion), and classify gauge theories with simple Lie algebras on non-spin manifolds. We also discuss the one-form symmetries of these theories and their ‘t Hooft anomalies. This talk is based on, jointly with J.P. Ang and Konstantinos Roumpedakis.

5/13/2020 Nathan Seiberg (IAS)

This meeting will be taking place virtually on Zoom.

Title: Continuum Quantum Field Theory for Fractons, Part I

Abstract:  Starting with a lattice system with local interactions at short distances, its long-distance behavior is captured by a continuum Quantum Field Theory (QFT).  This description is universal, i.e. it is independent of most of the details of the microscopic system. Surprisingly, certain recently discovered lattice systems, and in particular models of fractons, seem to violate this general dogma.  Motivated by this apparent contradiction, we will present exotic continuum QFTs that describe these systems. 
5/14/2020 Shu-Heng Shao (IAS) 

This meeting will be taking place virtually on Zoom.

Title: Continuum Quantum Field Theory for Fractons, Part II

Abstract:  Starting with a lattice system with local interactions at short distances, its long-distance behavior is captured by a continuum Quantum Field Theory (QFT).  This description is universal, i.e. it is independent of most of the details of the microscopic system. Surprisingly, certain recently discovered lattice systems, and in particular models of fractons, seem to violate this general dogma.  Motivated by this apparent contradiction, we will present exotic continuum QFTs that describe these systems.
5/20/2020David Tong (University of Cambridge)

This meeting will be taking place virtually on Zoom.

Title: Boundary States for Fermions: SPT Phases, RG Flows, and a Whole Bunch of Related Things.

Abstract: I’ll describe boundary conditions for fermions in d=1+1 dimensions, using the framework of boundary conformal field theory. I’ll explain how boundary states are classified by a mod 2 index, related to their SPT phase, describe how one can follow RG flows from one boundary state to another, and give a novel perspective on the Z_8 classification of d=2+1 SPT phases.
5/21/2020Yoshio Kikukawa (Institute of Physics, the University of Tokyo)

This meeting will be taking place virtually on Zoom.

Title: Gauge-invariant path-integral measure for the overlap Weyl fermions  in 16 of SO(10)

Abstract: We consider a lattice formulation of the SO(10) chiral gauge theory with left-handed Weyl fermions in the sixteen dimensional spinor representation 16  in the framework of the overlap fermion/the Ginsparg-Wilson relation.  We propose a manifestly gauge-invariant path-integral measure for the left-handed Weyl field on the lattice using all the components of the Dirac field, but the right-handed part of which is just saturated completely by inserting a suitable product of the SO(10)-invariant ‘t Hooft vertices in terms of the right-handed field. The definition of the measure applies to all possible topological sectors. The measure possesses all required transformation properties under lattice symmetries and the induced effective action is CP invariant. The global U(1) symmetry of the left-handed field is anomalous due to the non-trivial transformation of the measure, while that of the right-handed field is explicitly broken by the ’t Hooft vertices. There remains the issue of smoothness/locality in the gauge-field dependence of the Weyl fermion measure. 

We also discuss the relations of our formulation to other approaches/proposals to decouple the species-doubling/mirror degrees of freedom. Those include Eichten-Preskill model, Ginsparg-Wilson Mirror-fermion model, Domain wall fermion model with the boundary Eichten-Preskill term, and 4D Topological Insulator/Superconductor with gapped boundary phase. We clarify the similarity and the difference in technical detail and show that our proposal is a well-defined and unified testing ground for that basic question.
1:30 – 3:00pm
Dominic Williamson (Stanford) 

This meeting will be taking place virtually on Zoom.

Title: Non-Abelian fractons from gauged layers

Abstract: I will describe a construction of gapped 3D lattice models with non-Abelian fractons from gauging subsystem symmetries of topological layers. I will describe how this relates to previously constructed fracton models with nonabelian particles and explain how our construction fits into the recently developed picture of gapped fracton phases as topological defect networks. 
5/28/2020Hiroki Isobe (MIT)

This meeting will be taking place virtually on Zoom.

TitleSupermetal from a high-order Van Hove singularity

Abstract: A Van Hove singularity (VHS) of the density of states (DOS) is universal in a periodic system.  In two dimensions, a saddle point of energy dispersion yields a logarithmic divergence in the DOS.  Here, we introduce a new kind of VHS, motivated by the recent development of moiré materials.  We define a high-order VHS, which gives a power-law DOS divergence [1].  It requires only a single tuning parameter, such as a twist angle of a moiré material, pressure, and strain.  We further perform a renormalization group analysis near a high-order VHS to study the effect of electron interactions [2].  We reveal a nontrivial metallic state, where various divergent susceptibilities coexist, but no long-range order appears.  We call such a metallic state as a supermetal.  Our controlled analysis shows that a supermetal at the interacting fixed point is a non-Fermi liquid. 
6/3/2020Juan Maldacena (IAS)

This meeting will be taking place virtually on Zoom.

Title: Magnetic Black Holes

Abstract: We discuss properties of magnetically charged black holes in the Standard Model. We will discuss how the electroweak symmetry is restored around the black hole. In addition, the Hawking evaporation rate is greatly enhanced by a factor of the charge of the black hole. These provide interesting candidates for primordial black holes which can have a relatively low mass.
6/4/2020Sheng-Jie Huang (U Maryland)

This meeting will be taking place virtually on Zoom.

Title: Coupled layers, p-string condensate, and exactly solvable fracton models.

Abstract: In this talk, I will introduce a class of gapped fracton models, dubbed “cage-net fracton models”.  I will first review the coupled layer construction for exactly solvable fracton models. This construction leads to a general mechanism to obtain cage-net fracton models through a “p-string condensation”, where the extended one-dimensional particle strings built out of pointlike excitations are condensed. This p-string condensation generalizes the concept of anyon condensation in a conventional topological order and allows us to establish the properties of the fracton phase, such as its ground-state wave function, the spectrum and the mobility of excitations. To illustrate the main idea, I will focus on a simple example: doubled-Ising cage-net model. I will show that there are intrinsic non-Abelian excitations with restricted-mobility in this model and they cannot be understood as bound states among two-dimensional non-Abelian anyons and Abelian particles. If time permits, I will discuss another class of exactly solvable fracton models based on a generalization of the twisted gauge theory. 
8:30pm ET
Alexey Milekhin (IAS Princeton)

This meeting will be taking place virtually on Zoom.

Title: Traversable wormholes in four and two dimensions.

Abstract: In my talk I discuss traversable wormholes in four and two dimensions.
In four dimensions I present a solution based on two magnetically charged black holes. It is a solution of classical Einstein gravity which requires U(1) gauge field and massless fermions only and it does not need exotic matter or boundary conditions. It is a long wormhole that does not lead to causality violations in the ambient space Very similar wormholes in two dimensional Jackiw–Teitelboim(JT) gravity can be constructed in Sachdev–Ye–Kitaev(SYK) model, where one can study the real-time formation of the wormhole numerically. I will explain similarities
and differences between these four- and two-dimensional solutions and argue that in SYK the formation of the wormhole is smooth and takes time independent of N in the large N limit.

Based on arXiv: 1807.04726 and 1912.03276
6/11/2020Liujun Zou (Perimeter)

This meeting will be taking place virtually on Zoom.

Title: Symmetry enriched U(1) quantum spin liquids and beyond

Abstract: I will present our characterization and classification of 3+1 dimensional U(1) quantum spin liquids (QSLs) enriched by symmetries. These QSLs are spin system described by a deconfined U(1) gauge theory at low energies, and we assume that the only gapless degree of freedom is the photon. I will mostly focus on the example where the symmetry includes SO(3) spin rotation and time reversal, from which I will summarize our general scheme for the characterization and classification. The characterization and classification are based on the properties of the matters coupled to the emergent U(1) gauge field, although they are gapped. I will also discuss some applications of the ideas developed here to topological phases protected by crystalline symmetries. In order to avoid potential misunderstanding due to the difference in the ideology and language between physicists with different background, I will give an overview of these differences at the beginning of the talk.
6/17/2020Mithat Unsal (NCSU)

This meeting will be taking place virtually on Zoom.

Title: QCD(adj) and deformed Yang-Mills: From weak coupling confinement to adiabatic continuity

Abstract: More than 10 years ago, I showed that non-supersymmetric QCD with adjoint fermions admits  a (non thermal) compactification on $R^3 \times  S^1$ where non-perturbative gauge dynamics becomes calculable. The mass gap,  linear confinement and discrete chiral symmetry breaking  are sourced by magnetic bions,  which are correlated monopole-instanton anti-instanton pairs which have non-vanishing magnetic charge but have zero topological charge.  This construction led to the idea of the double-trace deformation of pure Yang Mills theory on $R^3 x S^1$, which is continuously connected to pure YM on $R^4$ in the sense of continuity of all gauge invariant order parameters. It turns out that all qualitative non perturbative properties of deformed YM theory are in agreement with all of our
non-perturbative expectations concerning pure YM theory.  Over the last year, numerical simulations have shown that the topological susceptibility of deformed YM on small $S^1 \times R^3$ are in precise agreement with the numerical results on large $S^1 \times R^3$. Therefore, it is very likely that there is more truth in deformed YM construction than that meets the eye.  I will give a lecture style talk on these topics.
6/18/2020Kevin Slagle (Caltech)

This meeting will be taking place virtually on Zoom.

Title: Foliated QFT and Topological Defect Networks of Fracton Order

Abstract: I will describe two new descriptions of gapped fracton topological order. These descriptions are generic and make minimal modifications to ordinary TQFT in order to obtain fracton physics. The first description constructs a fracton order by embedding a network of topological defects (aka interfaces) within an ordinary topological order, which results in the restricted fracton mobility. The second description takes the continuum limit by viewing the defect layers as infinitesimally separated. This is done by coupling a TQFT, such as BF theory, to a new kind of foliated gauge field. The first description is based on arXiv:2002.05166, while the second is based on a forthcoming work.
9:30 – 11:00am ET
Pavel Putrov (ICTP)

This meeting will be taking place virtually on Zoom.

Title: Holomorphic anomaly in Vafa-Witten theory

Abstract: Vafa-Witten theory is a topologically twisted version of 4d N=4 super Yang-Mills theory. In my talk I will tell how to derive a holomorphic
anomaly equation for its partition function on CP^2 by two different,
but somewhat analogous, methods. First is the derivation from the path
integral of the effective theory on the Coulomb branch. The second is
the derivation from the path-integral in the effective 2d theory
obtained by compactification of the corresponding 6d (2,0) theory on the
ternsor branch.
9:30 – 11:00am ET
Daniel Bulmash (University of Maryland)

This meeting will be taking place virtually on Zoom.

Title: Insights into type-II fractons via topological order

Abstract: “Type-II” fracton phases are exotic, gapped phases of matter in which all point-like excitations are deconfined but completely immobile. We present two approaches to constructing and analyzing models for type-II fractons using tools from conventional topological order. First, we use networks of defects in topological quantum field theories to describe Haah’s B code, which is a type-II fracton model. We use this fact as evidence for a conjecture that all fracton models can be described by a suitable defect network. Second, we show how gauging global symmetries of Abelian type-II fracton models produces new, exactly solvable models with non-Abelian type-II fractons, and we analyze the unusual excitations.
9:00 – 10:30am ET
Juven Wang (Harvard CMSA)

This meeting will be taking place virtually on Zoom. Joint seminar with Weizmann Institute of Science of Israel.

Title: “Mother” Effective Field Theory for Fractional Quantum Hall Systems near ν= 5/2

Abstract: We propose a unified effective field theory (EFT) of fractional quantum Hall systems near the filling fraction ν = 5/2 that flows to pertinent IR candidate phases, including non-abelian Pfaffian, anti-Pfaffian, and particle-hole Pfaffian states (Pf, APf, and PHPf). Our EFT has a 2+1d non-abelian Chern-Simons gauge theory coupled to four Majorana fermions by a discrete charge conjugation gauge field, with Gross-Neveu-Yukawa-Higgs terms. Including deformations via a Higgs condensate and fermion mass terms, we can map out a phase diagram with tunable parameters, reproducing the recently-proposed percolation picture and its gapless topological phase transitions. Our EFT sits at an energy scale above the IR phases (e.g., low energy topological field theories), but below the UV completion by electronic wavefunctions or on a lattice. Moreover, we find that Pf|APf domain walls have higher tension than domain walls in the PHPf phase. Then the former, if formed, may transition to the energetically-favored PHPf domain walls; this could, in turn, help further induce a bulk transition to PHPf. My talk is based on, jointly with Po-Shen Hsin, Ying-Hsuan Lin, and Natalie M. Paquette; and a prior work with Biao Lian.
9:00 – 10:30am ET
Debanjan Chowdhury (Cornell)

This meeting will be taking place virtually on Zoom.

Title: Deconfined metallic quantum criticality-I
Abstract: A number of strongly correlated electronic materials exhibit quantum criticality that does not fit into the conventional Landau-Ginzburg-Wilson paradigm of continuous phase transitions. Inspired by these experimental examples, I will discuss a new class of quantum phase transitions that describe a continuous transition between a Fermi liquid metal with a generic electronic Fermi surface and electrical insulators without Fermi surface of neutral excitations. Such phase transitions are described in terms of a finite density of fractionalized excitations coupled to emergent gauge fields. I will discuss various concrete examples of such gauge theories and describe their associated phase transitions using a renormalization group framework.  Remarkably, we find examples of continuous phase transitions between Landau Fermi liquid metals and insulators, where the quantum critical point hosts a non-Fermi liquid with a sharp Fermi surface but no long-lived quasiparticles. I will comment on the relevance of this new theoretical framework for some of the most pressing questions in the field of quantum matter
7/15/2020Cenke Xu (UCSB)

This meeting will be taking place virtually on Zoom.

Title: Interplay between two boundary effects

Abstract: We study the interplay between two nontrivial boundary effects: (1) the d-1 dimensional edge states of d-dimensional strongly interacting symmetry protected topological states, and (2) the boundary fluctuations of d-dimensional bulk quantum criticality. We also discuss states localized at an interface in a higher dimensional bulk, when the bulk undergoes a quantum phase transition. Using controlled analytical methods, we demonstrate that the interplay between the two different boundary effects leads to rich physics at the d-1 dimensional boundary, including new stable fixed points, and also an exotic quantum phase transition which cannot happen in a local d-1 dimensional system alone. Our analytical calculation is qualitatively consistent with recent numerical works on nonlocal quantum many body systems.
7/16/2020Liujun Zou (Perimeter Institute)

This meeting will be taking place virtually on Zoom.

Title: Deconfined metallic quantum criticality – II

Abstract: Along with some general remarks, the main goal of this talk is to discuss in detail a concrete setup for deconfined metallic quantum criticality in a self-contained manner. In particular, we propose that certain quantum Hall bilayers can host examples of a deconfined metal-insulator transition (DMIT), where a Fermi liquid (FL) metal with a generic electronic Fermi surface evolves into a gapped insulator (or, an insulator with Goldstone modes) through a continuous quantum phase transition. The transition can be accessed by tuning a single parameter, and its universal critical properties can be understood using a controlled framework. At the transition, the two layers are effectively decoupled, where each layer undergoes a continuous transition from a FL to a generalized composite Fermi liquid (gCFL). The thermodynamic and transport properties of the gCFL are similar to the usual CFL, while its spectral properties are qualitatively different. The FL-gCFL quantum critical point hosts a sharply defined Fermi surface without long-lived electronic quasiparticles. Immediately across the transition, the two layers of gCFL are unstable to forming an insulating phase. We discuss the topological properties of the insulator and various observable signatures associated with the DMIT. Some key ingredients of this proposal include Dirac-Chern-Simons theory, color superconductivity, dimensional decoupling, etc.
9:30 – 11:00am ET
Qing-Rui Wang (Yale University)

This meeting will be taking place virtually on Zoom.

Title: Domain Wall Decorations, Anomalies, and Fermionic SPT

Abstract: In the constructions of symmetry-protected topological (SPT) states, we usually decorate lower-dimensional states to higher codimensional domain walls of the system. In this talk, we will argue that domain wall decorations are basically equivalent to spectral sequences in algebraic topology. I will first illustrate this idea in bosonic systems, with explicit formulas for all differentials on all pages in the Lyndon-Hochschild-Serre spectral sequence. These results are useful in bosonic systems with Lieb-Schultz-Mattis (LSM) theorems, SPT-LSM theorems, and symmetry-enriched gauge theories. The second part of the talk will focus on fermionic SPT states. Using domain wall decorations, we will give a systematic construction and classification of fermionic SPT states in 3+1 or lower dimensions. We can obtain the full classifications for arbitrary finite unitary Abelian symmetries and interacting 10-fold way. All the classifications are consistent with known results from other approaches such as point/loop braiding statistics and spin cobordisms.

9:30 – 11:00am ET
Kazuya Yonekura (Tohoku Univ, Japan)

This meeting will be taking place virtually on Zoom.

TitleNonperturbative anomaly inflow for fermions and p-form fields

Abstract: I will talk about a nonperturbative formulation of chiral fermions and chiral (self-dual) p-form fields, in terms of massive theories in one-higher dimensions. The introduction of the higher dimensional bulk is unavoidable due to the existence of anomalies, and I discuss the modern understanding of anomalies which appears very naturally in our formulation of chiral theories.
9:30 – 11:00am ET
Zheng-Cheng Gu (CUHK)

This meeting will be taking place virtually on Zoom.

TitleTopological qauntum field theory in 3+1D and a potential origin of dark matter
Abstract: Topological qauntum field theory(TQFT) is a very powerful theoretical tool to study topological phases and phase transitions. In 2 + 1D, it is well known that the Chern-Simons theory captures all the universal topological data of topological phases, e.g., quasi-particle braiding statistics, chiral central charge and even provides us a deep insight for the nature of topological phase transitions. Recently, topological phases of quantum matter are also intensively studied in 3 + 1D and it has been shown that loop like excitation obeys the so-called three-loop-braiding statistics. In this talk, I will discuss a TQFT framework to understand the quantum statistics of loop like excitation in 3 + 1D. Most surprisingly, 
this new class of 3+1D TQFT even provides us a new route towards understanding quantum gravity. I will also discuss a generalized Einstein  equation which might naturally include dark matter sector.
Friday, 3:00-4:30pm ET
Giandomenico Palumbo (Universit´e Libre de Bruxelles)

This meeting will be taking place virtually on Zoom.

Title: Fermion-fermion dualities in 3+1 dimensions

Abstract: Dualities play an important role in both quantum field theories and condensed matter systems. They can map hard-to-solve, interacting theories to free, non-interacting ones often trigger a deeper understanding of the systems to which they apply. Recently, a web of (non-supersymmetric) dualities has been discovered in 2+1 dimensions inspired by novel developments in topological phases of matter.
In this talk, I will present some extensions of the original 2+1-dimensional fermion-fermion duality in 3+1 dimensions and in presence of axial gauge fields. By employing the slave-rotor approach in the lattice, I will show the central role of the Kalb-Ramond field and chiral anomaly in their formulation. Finally, I will present some applications of these novel dualities in topological systems such as Weyl and Dirac semimetals and non-symmorphic topological insulators.
*Rescheduled Date*
Aleksey Cherman (University of Minnesota Minneapolis)

TitleHiggs-confinement phase transitions with fundamental representation matter

Abstract: I will discuss the conditions under which Higgs and confining regimes in gauge theories with fundamental representation matter fields can be sharply distinguished. It is widely believed that these regimes are smoothly connected unless they are distinguished by the realization of global symmetries.  However, I will show that when a U(1) global symmetry is spontaneously broken in both the confining and Higgs regimes, the two phases can be separated by a phase boundary.  The phase transition between the two regimes may be detected by a novel topological vortex order parameter. I’ll illustrate these ideas by explicit calculations in gauge theories in three spacetime dimensions, and then explain the generalization to four dimensions. One important implication of our results is that nuclear matter and quark matter are sharply distinct phases of QCD with an approximate SU(3) flavor symmetry.    
9:30 – 11:00am ET
Mirjam Cvetic (UPenn)

This meeting will be taking place virtually on Zoom.

Title: F-theory, Part I: Construction of Particle Physics Models

Abstract: We present recent advances in constructions of globally consistent F-theory compactifications which result in the exact chiral spectrum of the three-family Standard Models.  We highlight geometric tools to determine the gauge degrees, including continuous and discrete Abelian symmetries. We also outline techniques that determine the chiral matter spectrum.  We present the first examples of such constructions and then turn to a subsequent systematic exploration of the landscape of F-theory three-family Standard Models with a gauge coupling unification. We also outline recent progress toward calculations of Yukawa couplings and calculations of the number of charged-vector matter pairs.
9:30 – 11:00am ET
Ling Lin (CERN)This meeting will be taking place virtually on Zoom.

Title: F-theory, Part II: Global Structures from Arithmetics

Abstract: Many salient features of elliptic fibrations leave intriguing imprints on the physics of F-theory compactifications. In this talk, we will focus on the Mordell—Weil group of sections. Beyond the well-known relationship to abelian gauge symmetries, we will discuss how the global structure of the gauge group, e.g., the Standard Model [SU(3) x SU(2) x U(1)]/Z6, is encoded in the geometry. By re-interpreting a non-trivial global structure as having gauged 1-form center symmetries, we will further explain how geometric restrictions of having Mordell—Weil torsion can be understood field theoretically as anomalies of 1-form symmetries. A comparison between these anomalies and elliptic K3 surfaces points towards String Universality for 1-form center symmetries in 8d.
9:30 – 11:00am
Frank Wilczek (MIT, Arizona State, Jiao Tong, Stockholm)

This meeting will be taking place virtually on Zoom.

Title: Physical Approaches to Quantum Computing
9:30 – 11:00am ET

Ho Tat Lam (Princeton)

This meeting will be taking place virtually on Zoom.

Title: Discrete Theta Angles, Symmetries and Anomalies

Abstract: Gauge theories often admit discrete theta angles. Theories with different discrete theta angles can be constructed by gauging a global symmetry in a parent theory with different additional symmetry protected topological (SPT) phases. I will discuss how the global symmetries of these theories and their ‘t Hooft anomalies are controlled by the SPT phases. I will then present examples in various dimensions that exhibit two-group symmetries and non-invertible symmetries. The talk is based on in collaboration with Po-Shen Hsin.

Fall 2019:

9/05/2019Juven Wang (Harvard CMSA)Title: Quantum Matter Basics for Mathematicians
9/18/2019Po-shen Hsin (Caltech)



Title: Lorentz symmetry fractionalization and duality in (2+1)d


Abstract: I will introduce a discrete transformation in bosonic QFTs with Z2 one-form symmetry using the concept of symmetry fractionalization in condensed matter physics. I will then discuss some applications including boson/fermion dualities in (2+1)d.

9/19/2019Poshen Hsin (Caltech)Title: “3d duality”


Members’ Seminar

Ryohei Kobayashi (U of Tokyo)Title: Fermionic phases of matter on unoriented spacetime
9/25/2019Juven Wang (CMSA)



Title: Higher-Rank Tensor Field Theory of Non-Abelian Fracton and Embeddon


Abstract: We introduce a new class of tensor field theories in any dimension that has an interesting mixing between symmetric-tensor gauge theory and anti-symmetric tensor topological field theory. The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory may be a new gem sitting in the virgin territory outside the familiar gauge theories — outside the paradigm of Maxwell theory in 1865 and Yang-Mills theory in 1954. We discuss its relation to the non-abelian generalization of Fracton in condensed matter, and Embeddon that we will introduce. This is based on, jointly with Kai Xu (Harvard).

9/26/2019Shu-Heng Shao (IAS)



Title: Anomalies and Charged Operators


Abstract: We study the implications of ‘t Hooft anomaly for conformal field theory. Using the modular bootstrap, universal bounds on (1+1)-dimensional bosonic conformal field theories with an internal Z2 global symmetry are derived. We find that there is a universal upper bound on the lightest Z2 odd operator if the symmetry is anomalous, but there is no bound if the symmetry is non-anomalous.

We further discuss the implications for the Weak Gravity Conjecture in AdS3/CFT2.  Finally we present a conjecture on more general anomalies that cannot be matched by TQFTs, a notion known as the “symmetry-protected gaplessness” in condensed matter physics.




Zhen Bi (MIT) 



Title: Novel quantum criticality beyond Landau-Ginzburg-Wilson-Fisher paradigm


Abstract: The infrared behavior of 3 + 1-D non-abelian gauge fields with massless matter fields is an extremely important and intensively studied topic in particle physics. In this talk, we asking the following question from a condensed matter perspective: given some deconfined gauge theory in 3 + 1-D, what phase transition can this theory describe? It turns out to be a fruitful way to think about these gauge theories and provides many explicit examples for several novel quantum critical phenomena. 1. We present several examples of Deconfined Quantum Critical Points (DQCP) between Symmetry Protected Topological phases in 3 + 1-D for both bosonic and fermionic systems. 2. We find situations in which the same phase transition allows for multiple universality classes controlled by distinct fixed points. 3. We exhibit the possibility – which we dub “unnecessary quantum critical points” – of stable generic continuous phase transitions within the same phase. 4. We present examples of interaction driven band-theory forbidden continuous phase transitions between two distinct band insulators. 5. We find an example for a Landau-allowed quantum phase transition, however, with a critical theory that is beyond Landau description.

10/3/2019Ryan Thorngren (CMSA)



Title: Domain Walls and the CPT Theorem


Abstract: I will describe how in a relativistic quantum field theory, symmetry-broken domain walls enjoy a curious remnant of the broken symmetry obtained by a combination with the unbreakable CPT symmetry. There is an anomaly-matching condition relating the symmetry-preserving bulk phase to the anomaly on the wall. This condition is related to an interesting property of manifold cobordisms called the Smith isomorphism. I will prove some generalizations of the Smith isomorphism theorem and discuss some physics applications to superfluids and gauge theories. This is joint work with Itamar Hason and Zohar Komargodski.

10/4/2019Liang Kong (Shenzhen Institute of Quantum Sciences and Engineering, Southern University of Science and Technology) 



Title: A unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders


Abstract: It was well known that a gapless boundary of a 2+1D topological order is different from and significantly richer than a gapped boundary. In this talk, however, we will propose a unified mathematical theory of both gapped and gapless boundaries of 2+1D topological orders. In particular, we will show that observables on the 1+1D world sheet of a chiral gapless boundary in the long wave length limit form an enriched fusion category, the Drinfeld center of which is precisely the unitary modular tensor category associated to the bulk. If time permits, we will also briefly discuss some consequences of this result, including a theory of non-chiral gapless boundaries, applications to boundary topological phase transitions, 0+1D defects between different gapless boundaries and a generalized boundary-bulk relation. This is joint work with Hao Zheng.

10/9/2019Peter Koroteev (Berkeley) 



Title: On Quiver W-algebras and Defects from Gauge Origami


Abstract: Using Nekrasov’s gauge origami framework, we study two different versions of the BPS/CFT correspondence – first, the standard AGT duality and, second, the quiver W algebra construction which has been developed recently by Kimura and Pestun. The gauge origami enables us to work with both dualities simultaneously and find exact matchings between the parameters. In our main example of an A-type quiver gauge theory, we show that the corresponding quiver qW-algebra and its representations are closely related to a large-n limit of spherical gl(n) double affine Hecke algebra whose modules are described by instanton partition functions of a defect quiver theory.

10/10/2019Julio Parra Martinez (UCLA)



Title: GSO projections and D-brane classification via SPT phases


Abstract: I will explain how a choice of fermionic SPT phases on the string worldsheet gives rise to the different GSO projections. This point of view not only easily explains why there are essentially two type II and 0 theories, but also predicts an eight-fold classification of unoriented Pin- type 0 theories. A similar analysis for unoriented Type II strings requires introducing Double Pin (DPin) structures, and confirms that there is an essentially unique choice of the type I worldsheet theory. By considering the implications of the bulk SPTs on the boundary of opens strings we provide an alternative route to the K-theoretic classification of D-branes, and clarify some of their properties. As an example, I will describe the classification of D-branes in the unoriented Pin- type 0 theories, in which all higher real K-groups play a role.




Kantaro Ohmori (SUNY SCGP)Title: Anomaly Obstructions to Symmetry Preserving Gapped Phases: Discrete symmetry case



Abstract: Anomalies are renormalization group invariants and constrain the dynamics of quantum field theories. In this talk we show that certain anomalies for discrete global generalized symmetries imply that the underlying theory either spontaneously breaks its global symmetry or is gapless. This is done by observing that a symmetry preserving unitary TQFT is not compatible with the anomaly whose inflow action evaluates nontrivially on a certain manifold.

10/17/2019No Seminar 
10/23/2019 Chong Wang (Perimeter)



Title: Unquantized quantum anomalies: electric polarization, Luttinger theorem and correlated Weyl semimetals
10/24/2019Andrew Turner (MIT) 



Title: General F-theory models with SU(3) x SU(2) x U(1) / Z_6 symmetry


Abstract: We construct a general form for an F-theory Weierstrass model over any base giving a 6D or 4D supergravity theory with gauge group SU(3) x SU(2) x U(1) / Z_6 and associated generic matter. The concept of ‘generic matter’ can be rigorously defined in 6D supergravity and generalizes naturally to four dimensions for F-theory models. We describe general F-theory models with this gauge group and the associated generic matter content, which fit into two distinct classes, and present an explicit Weierstrass model that realizes these models as two distinct branches. We also discuss, as a special case, the class of models recently studied by Cvetic, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing.




Chong Wang (Perimeter) Title: A theory of deconfined pseudo-criticality
10/31/2019Patrick Lee (MIT)



Title: Gapless spin liquid and emergent gauge theory


Abstract: I shall review the emergence of gauge theory as a description of quantum spin liquid, particularly the gapless variety. The matter field plays a key role in stabilizing the deconfined phase. I shall also discuss the current experimental status of gapless spin liquid candidates, including the recently “re-discovered” example of TaS2.

11/6/2019Dan Freed (UT Austin)



Title: M-theory is time-reversal invariant


Abstract: In joint work with Mike Hopkins we prove that there is no parity anomaly in M-theory in the low-energy field theory approximation. There are two sources of anomalies: the Rarita-Schwinger field and the cubic form for the C-field. I will explain the general principles behind these anomalies, since they apply in many problems. Then I’ll turn to the specific computations we did to verify this anomaly cancellation. They include topologial and geometric methods for computing eta-invariants as well as homotopy-theoretic techniques for computing bordism groups.

11/7/2019Mathias Scheurer (Harvard)Title: Gauge theories for the cuprates:thermal Hall effect and optimal doping


Abstract: Recent experiments [1] have revealed an enhanced thermal Hall effect in the pseudogap phase of several different cuprate compounds. The large signal even persists in the undoped system and, thus, challenges our understanding of the square-lattice antiferromagnet fundamentally. In the first part of the talk, I will analyze possible mechanisms that can give rise to a thermal Hall effect in the antiferromagnet [2,3]. In particular, I will discuss the possibility [3] that the magnetic field can drive the Néel state close to a transition to a phase where Néel order coexists with a chiral spin liquid. A spinon lattice model for this transition is shown to give rise to a large thermal Hall conductivity that also features a magnetic-field and temperature dependence similar to experiment. We will derive the low-energy continuum field theory for the transition, which is characterized by an emergent global SO(3) symmetry and has four different formulations that are all related by dualities. If time permits, I will present, in the second part of the talk, a non-Abelian gauge theory that we propose [4] as an effective field theory for the cuprates near optimal doping. In this theory, spin-density-wave order is fractionalized into Higgs fields while all low-energy fermionic excitations are electron-like and gauge neutral. The conventional Fermi-liquid state corresponds to the confining phase of the theory at large doping and there is a quantum phase transition to a Higgs phase, describing the pseudogap, at low doping. It will be shown that the topological order of the Higgs phase is very naturally intertwined with charge-density-wave, Ising-nematic, and scalar spin-chirality order. We will also discuss the quantum critical point of the model.




Michael Pretko (U Colorado)Title:  Introduction to Fractons


Abstract:  A fracton is an exotic new type of emergent quasiparticle with restricted mobility.  While a single fracton is strictly immobile in isolation, they can often come together to form certain mobile bound states.  In this talk, I will give a bird’s-eye overview on the current state of the field of fractons. I will begin with the theoretical formalism for fractons in terms of symmetric tensor gauge theories, which possess unusual higher moment conservation laws.  I will then outline some physical realizations of fractons, such as spin models and topological crystalline defects, the latter of which arises through a novel field theory duality. Finally, I will discuss some of the most interesting phenomenology of fracton systems, such as their non-ergodic and gravitational behavior.




Michael Pretko (U Colorado)Title:  Advances in Fracton Physics: Dualities, Field Theories, and Classification


Abstract:  In this talk, I will give short informal explanations of three topics in the field of fractons with some interesting mathematical structure.  I will begin with a detailed discussion of fracton-elasticity duality, relating the properties of tensor gauge theories to the elastic description of two-dimensional crystals.  I will emphasize the role of symmetries in this duality, and also discuss how the duality extends to three dimensions, giving rise to “higher-form” analogues of fracton conservation laws.  Next, I will discuss recent advances on the field theory description of fractons, showing how fractons can be obtained by gauging field theories with a “vector” global symmetry. Finally, I will describe recent work towards classifying fracton phases in terms of their fusion theory, which can be described as a module over the group ring of translations.

11/20/2019Subir Sachdev (Harvard)



Title: Models of optimal doping criticality in the cuprate superconductors


Abstract: There is now much experimental evidence for a significant change in the electronic structure of cuprate superconductors near a hole doping p=p_c optimal for superconductivity. Only for p > p_c do the electronic properties agree with the predictions of band theory. We argue that the data supports the existence of a quantum critical point (QCP) at p=p_c, and for p < p_c we have a novel state characterized by emergent gauge fields, possibly co-existing with conventional symmetry breaking orders. We present evidence that such a QCP is present in the Hubbard model with random, and all-to-all, hopping and exchange. We also discuss a SU(2) gauge theory for the QCP in model of fluctuating incommensurate spin density waves in the absence of disorder.

11/21/2019Natalie Paquette (Caltech)



Title: Koszul duality in field theory & holography
11/25/2019Yu-An Chen (Caltech)



Title:  Exact bosonization in higher dimensions and the duality between supercohomology fermionic SPT and higher-group bosonic SPT phases


Abstract: The first part of this talk will introduce generalized Jordan–Wigner transformation on arbitrary triangulation of any simply connected manifold in 2d, 3d and general dimensions. This gives a duality between all fermionic systems and a new class of lattice gauge theories. This map preserves the locality and has an explicit dependence on the second Stiefel–Whitney class and a choice of spin structure on the manifold. In the Euclidean picture, this mapping is exactly equivalent to introducing topological terms (Chern-Simon term in 2d or the Steenrod square term in general) to the Euclidean action. We can increase the code distance of this mapping, such that this mapping can correct all 1-qubit and 2-qubits errors and is useful for the simulation of fermions on the quantum computer. The second part of my talk is about SPT phases. By the boson-fermion duality, we are able to show the equivalent between any supercohomology fermionic SPT and some higher-group bosonic SPT phases. Particularly in (3+1)D, we have constructed a unitary quantum circuit for any supercohomology fermionic SPT state with gapped boundary construction. This fermionic SPT state is derived by gauging higher-form symmetry in the higher-group bosonic SPT and ungauging the fermion parity. The bulk-boundary correspondence in (3+1)D fermion SPT phases will also be briefly discussed.

11/27/2019Meng Cheng (Yale) 



Title: Gapped boundary of symmetric topological phases and relative anomalies in (1+1)d CFTs


Abstract: Many (2+1)d topological phases admit gapped boundaries. In the presence of global symmetry, the classification of symmetric boundary conditions is further enriched. I will discuss recent work on classifying such boundary conditions for a doubled topological phase, and a general construction of such boundaries in symmetry-enriched string-net models using module categories. I will also describe how the results can be used to compute relative ’t Hooft anomalies in (1+1)d CFTs algebraically.

12/3/2019Quantum Matter workshop 
12/5/2019Yizhi You (Princeton)



Title: Emergent fractons and algebraic quantum liquid from plaquette melting transitions


Abstract: Paramagnetic spin systems with spontaneously broken spatial symmetries, such as valence bond solid (VBS) phases, can host topological defects carrying non-trivial quantum numbers, which enables the paradigm of deconfined quantum criticality. In this talk, I will show that the defects of the valence plaquette solid(VPS) order parameter, in addition to possessing non-trivial quantum numbers, have fracton mobility constraints in the VPS phase. The spinon inside a single vortex cannot move freely in any direction, while a dipolar pair of vortices with spinon pairs can only move perpendicular to its dipole moment. These mobility constraints, while they persist near QCP, can potentially inhibit the condensation of spinons and preclude a continuous transition from the VPS to the Néel antiferromagnet. Instead, the VPS melting transition can be driven by the proliferation

of spinon dipoles. In particular, we argue that a 2d VPS can melt into a stable gapless phase in the form of an algebraic bond liquid with algebraic correlations and long-range entanglement. Such a bond liquid phase yields a concrete example of the elusive 2d Bose metal with symmetry fractionalization.





Nick G. Jones (University of Bristol)Title: Toeplitz determinants and correlations in topological quantum chains


Abstract: Topological phases protected by symmetry can occur in both gapped and critical systems. I will discuss recent work on such phases for non-interacting fermions in one dimension with spinless time-reversal symmetry. I will show how the phases are classified by a topological invariant and a central charge, explaining also the connection to edge modes. The bulk order parameters of these phases are correlators of fermionic string operators. I will explain how to derive exact asymptotics of these correlation functions using Toeplitz determinant theory, giving insight into the interplay between topology and criticality.

This is largely based on the papers:

Asymptotic correlations in gapped and critical topological phases of 1D quantum systems, N. G. Jones and R. Verresen, J. Stat. Phys. 175 (2019)

Topology and edge modes in quantum critical chains, R. Verresen, N. G. Jones and F. Pollmann, Phys. Rev. Lett. 120 (2018)

12/11/2019Yuya Tanizaki (NCSU)



Title: Constraints on possible dynamics of QCD by symmetry and anomaly



Abstract: Low-energy dynamics of Quantum Chromodynamics (QCD) is an important subject for nuclear and hadron physics, but it is a strongly coupled system and difficult to solve. In this situation, symmetry and also anomaly give us an important guide to make a solid conclusion onpossible behaviors of QCD. We find a new discrete anomaly in massless QCD, which says that the baryon number current is anomalously broken under the background gauge field for vector-like flavor symmetry and discrete axial symmetry. To match this anomaly in the chiral-symmetry broken phase, the existence of baryons as Skyrmions is mandatory, and Skyrmion current must show the same anomaly. This is satisfied in the ordinary scenario of chiral symmetry breaking, but not satisfied in an exotic scenario of chiral symmetry breaking proposed by Stern about two decades ago. Since the anomaly matching is applicable even with the sign problem, Stern phase is excluded even for the finite-density QCD at zero temperatures.


12/12/2019Yuya Tanizaki (NCSU)



Title: Modifying instanton sums in QCD



Abstract: In the path integral formulation, we need to sum up all possible field configurations to define a QFT. If the configuration space is disconnected, we must specify how they should be summed by giving extra data to specify the QFT. In this talk, we try to restrict the possible number of instantons in SU(N) gauge theories, Yang-Mills theory and QCD, and we find out the vacuum structures of them. For consistency with locality, we have to introduce an extra topological degrees of freedom, and the theory acquires the 3-form symmetry. The existence of this 3-form symmetry leads to extra vacua, and moreover it turns out to give an interesting selection rule for the domain-wall excitation/vacuum decay. 




Artan Sheshmani (Harvard CMSA)



Title: Higher rank flag sheaves and Vafa-Witten invariants


Abstract: We study moduli space of holomorphic triples $f: E_{1} \rightarrow E_{2}$, composed of (possibly rank $>1$) torsion-free sheaves $(E_{1}, E_{2})$ and a holomorphic map between them, over a smooth complex projective surface $S$. The triples are equipped with a Schmitt stability condition. We prove that when the Schmitt stability parameter becomes sufficiently large, the moduli space of triples benefits from having a perfect relative and absolute obstruction theory in some cases (depending on Chern character of $E_{1}$). We further generalize our construction to higher-length flags of higher rank sheaves by gluing triple moduli spaces, and extend earlier work, with Gholampur and Yau, where the obstruction theory of nested Hilbert schemes over the surface was studied. Here we extend the earlier results to the moduli space of flags $E_{1}\rightarrow E_{2}\rightarrow \cdots \rightarrow E_{n}$, where the maps are injective (by stability). There is a connection, by wall-crossing in the master space, developed by Mochizuki, between the theory of such higher rank flags, and the theory of Higgs pairs on the surface, which provides the means to relate the flag invariants to the local DT invariants of any threefold given by a line bundle over the surface, $X :={\rm Tot}(L \rightarrow S)$. The latter DT invariants, when L is the canonical bundle of S, contribute to Vafa-Witten invariants. Joint work with Shing-Tung Yau, arXiv:1911.00124.

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