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 11:50-1:00pm in CMSA, G10. The schedules for both seminars will be updated below as speakers are confirmed:

Date Speaker Title/Abstract


Juven Wang (Harvard CMSA)

Title: Quantum Matter Basics for Mathematicians


Po-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.


Poshen Hsin (Caltech)

Title: “3d duality”


Members’ Seminar

Ryohei Kobayashi (U of Tokyo)

Title: Fermionic phases of matter on unoriented spacetime


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


Shu-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.


Ryan 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.


Liang 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.


Peter 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.


Julio 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.


No Seminar



Chong Wang (Perimeter)


Title: Unquantized quantum anomalies: electric polarization, Luttinger theorem and correlated Weyl semimetals


Andrew 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


Patrick 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.


Dan 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.


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.



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.


Subir 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.


Natalie Paquette (Caltech)

Title: Koszul duality in field theory & holography


Yu-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 \mathbb{Z}_2 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 \mathbb{Z}_2 fermion parity. The bulk-boundary correspondence in (3+1)D fermion SPT phases will also be briefly discussed.


Meng Cheng (Yale) 



Quantum Matter workshop



Yizhi You (Princeton)



Yuya Tanizaki (NCSU)









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