# Quantum Matter/Condensed Matter Seminars

As part of the program on Quantum Matter in Mathematics and Physics, the CMSA will be hosting two weekly seminars. The Quantum Matter/Quantum Field Theory seminar will take place on  Wednesdays from 10:30 – 12:00pm in CMSA G10.  The Condensed Matter/Math Seminar will take place on Thursdays from 10:30 – 12:00pm in CMSA, G10. The schedules for both seminars will be updated below as speakers are confirmed:

#### Spring 2020:

Date Speaker Title/Abstract
2/5/2020 Ya-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.

2/6/2020 Yuan Cao (MIT)
2/12/2020 Xue-Yang Song (Harvard)
2/13/2020 Grigory Tarnopolskiy (Harvard)
2/19/2020
2/20/2020
2/26/2020
3/4/2020

G02

3/5/2020

G02

3/11/2020
3/12/2020
3/18/2020
3/19/2020

G02

3/25/2020

G02

3/26/2020
4/1/2020
4/2/2020
4/8/2020

G02

4/9/2020

G02

4/15/2020
4/16/2020
4/22/2020
4/23/2020
4/29/2020

G02

4/30/2020

G02

5/6/2020 Quantum Matter Workshop
5/7/2020
5/13/2020

G02

5/14/2020

G02

#### Fall 2019:

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

Video

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.

9/19/2019 Poshen Hsin (Caltech) Title: “3d duality”
9/20/2019

Members’ Seminar

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

Video

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 https://arxiv.org/abs/1909.13879, jointly with Kai Xu (Harvard).

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

Video

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.

10/2/2019

Zhen Bi (MIT)

Video

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.

10/3/2019 Ryan Thorngren (CMSA)

Video

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.

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

Video

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.

10/9/2019 Peter Koroteev (Berkeley)

Video

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.

10/10/2019 Julio Parra Martinez (UCLA)

Video

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.

10/16/2019

G02

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.

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

Video

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

Video

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.

10/30/2019

G02

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

Video

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.

11/6/2019 Dan Freed (UT Austin)

Video

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.

11/7/2019 Mathias 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.

11/13/2019

G02

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.

11/14/2019

G02

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.

11/20/2019 Subir Sachdev (Harvard)

Video

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.

11/21/2019 Natalie Paquette (Caltech)

Video

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

Video

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.

11/27/2019 Meng Cheng (Yale)

Video

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.

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

Video

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.

12/6/2019

1:00pm

CMSA G02

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)

12/11/2019 Yuya Tanizaki (NCSU)

Video

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.

12/12/2019 Yuya Tanizaki (NCSU)

Video

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.

12/18/2019

12:00pm

Artan Sheshmani (Harvard CMSA)

Video

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.