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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

A 6-year journey: from gravitational anomaly to a unified theory of generalized symmetry
2023-09-08 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Xiao-Gang Wen (MIT)
Title: A 6-year journey: from gravitational anomaly to a unified theory of generalized symmetry
Abstract: Emergent symmetry can be generalized symmetry beyond (higher) group description and/or can be anomalous. I will describe a unified theory for generalized symmetry based on symmetry/topological-order correspondence. I will also discuss some applications of emergent generalized symmetry.

Anomalies of Non-Invertible Symmetries
2023-09-13 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Clay Córdova (U Chicago)
Title: Anomalies of Non-Invertible Symmetries

Floquet codes, automorphisms, and quantum computation
2023-09-22 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Margarita Davydova (MIT)
Title: Floquet codes, automorphisms, and quantum computation
Abstract: In this talk, I will introduce a new kind of measurement-based quantum computation inspired by Floquet codes. In this model, the quantum logical gates are implemented by short sequences of low-weight measurements which simultaneously encode logical information and enable error correction. We introduce a new class of quantum error-correcting codes generalizing Floquet codes that achieve this, which we call dynamic automorphism (DA) codes.
As in Floquet codes, the instantaneous codespace of a DA code at any fixed point in time is that of a topological code. In this case, the quantum computation can be viewed as a sequence of time-like domain walls implementing automorphisms of the topological order, which can be understood in terms of reversible anyon condensation paths in a particular parent model. This talk will introduce all of these concepts as well as provide a new perspective for thinking about Floquet codes.
The explicit examples that we construct, which we call DA color codes, can implement the full Clifford group of logical gates in 2+1d by two- and, rarely three-body measurements. Using adaptive two-body measurements, we can achieve a non-Clifford gate in 3+1d, making the first step towards universal quantum computation in this model.
The talk is based on recent work with Nathanan Tantivasadakarn, Shankar Balasubramanian, and David Aasen [arxiv: 2307.10353].

Quantum field theory approach to quantum information
2023-09-28 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Cenke Xu (UCSB)
Title: Quantum field theory approach to quantum information
Abstract: We apply the formalism of quantum field theory and Euclidean space-time path integral to investigate a class of quantum information problems. In particular, we investigate quantum many-body systems under weak-measurement and decoherence. The Euclidean space-time path integral allows us to map this problem to a quantum field theory with (temporal) boundary or defects. We therefore investigate two types of quantum many-body systems with nontrivial boundary physics: quantum critical points, and states with nontrivial topology, such as Chern insulator and symmetry protected topological states. For example, we demonstrate that a Wilson-Fisher quantum critical point can be driven into an “extraordinary-log” phase after weak-measurement. Another example is that, we argue that a system with higher form symmetry may be driven to a self-dual phase transition under weak measurement.

Non-invertible symmetries, leptons, quarks, and why multiple generations
2023-10-11 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Seth Koren (Notre Dame)
Title: Non-invertible symmetries, leptons, quarks, and why multiple generations
Abstract: Generalized global symmetries are present in theories of particle physics, and understanding their structure can give insight into these theories and UV completions thereof. After discussing the generalized symmetries of the Standard Model, we will go Beyond and show that the identification of a non-invertible symmetry of Z’ models of L_µ – L_τ reveals the existence of non-Abelian horizontal gauge theories which naturally produce exponentially small Dirac neutrino masses. Next we will uncover a subtler non-invertible symmetry in horizontal gauge theories of the quark sector which will lead us to a massless down-type quarks solution to strong CP in color-flavor unification. Intriguingly, this theory works by virtue of the SM having the same numbers of colors and generations.

Landscape of quantum phases in quantum materials
2023-11-02 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint Quantum Matter in Mathematics and Physics and Topological Quantum Matter Seminar
Speaker: Liujun Zou (Perimeter Institute)
Title: Landscape of quantum phases in quantum materials

Abstract: A central goal of condensed matter physics is to understand which quantum phases of matter can emerge in a quantum material. For this purpose, one should be able to not only describe the quantum phases using some effective field theories, but also capture the important microscopic information of the material via mathematical formulation. In this talk, I will present a framework to classify quantum phases in quantum materials, where the microscopic information of a material is encoded in its quantum anomaly. I will talk about the application of this framework to classify various exotic quantum phases of matter in different lattice systems. Using our framework, we have obtained many results unexpected from the previous literature.

A Long Exact Sequence in Symmetry Breaking
2023-11-07 16:30 - 18:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Cameron Krulewski (MIT) and Leon Liu (Harvard)
Title: A Long Exact Sequence in Symmetry Breaking
Abstract: We study defects in symmetry breaking phases, such as domain walls, vortices, and hedgehogs. In particular, we focus on the localized gapless excitations that sometimes occur at the cores of these objects. These are topologically protected by an ’t Hooft anomaly. We classify different symmetry breaking phases in terms of the anomalies of these defects and relate them to the anomaly of the broken symmetry by an anomaly-matching formula. We also derive the obstruction to the existence of a symmetry breaking phase with a local defect. We obtain these results using a long exact sequence of groups of invertible field theories, which we call the “symmetry breaking long exact sequence” (SBLES).
The mathematical backbone of the SBLES is the Smith homomorphism, which gives a family of maps between twisted bordism groups. Though many examples have been studied, we give the first completely general account of the Smith homomorphism. We lift it to a map of Thom
spectra and identify the cofiber, producing a long exact sequence of twisted bordism groups; the SBLES is the Anderson dual of that long exact sequence. Our work develops further the theory of higher Berry phase and its bulk-boundary correspondence and serves as a new computational tool for classifying symmetry protected topological phases.

Modulated Gauge Theories and Fracton Behavior in 2D
2023-11-22 16:00 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter Seminar
Speaker: Guilherme Delfino Silva (Boston University)
Title: Modulated Gauge Theories and Fracton Behavior in 2D
Abstract: In this talk we investigate deconfined phases of two-dimensional ZN lattice gauge theories associated to spatially modulated symmetries. In order to study the low-energy physics of such modulated gauge theories we propose and explore exactly solvable gapped Hamiltonians, which allow us to fully characterize their low-energy properties at zero temperature. We provide explicit examples and discuss how non-polynomial symmetries, as exponential symmetries, are powerful enough to fully constrain the mobility of isolated excitations.

A Plane Defect in the 3d O(N) Model
2023-12-01 16:30 - 17:30 | Hybrid
Quantum Matter Seminar
Speaker: Abijith Krishnan (MIT)
Title: A Plane Defect in the 3d O(N) Model
Abstract: It was recently found that the classical 3d O(N) model in the semi-infinite geometry can exhibit an “extraordinary-log” boundary universality class, where the spin-spin correlation function on the boundary falls off as (log x)^(-q). This universality class exists for a range 2≤N<Nc and Monte-Carlo simulations and conformal bootstrap indicate Nc>3. In this talk, I’ll extend this result to the 3d O(N) model in an infinite geometry with a plane defect. I’ll explain using the renormalization group (RG) that the extraordinary-log universality class is present for any finite N≥2, and that a line of defect fixed points is present at N=∞. This line of defect fixed points is lifted to the ordinary, special (no defect) and extraordinary-log universality classes by 1/N corrections. I’ll show that the line of defect fixed points and the 1/N corrections agree with an a-theorem by Jensen and O’Bannon for 3d CFTs with a boundary. Finally, I’ll conclude by noting some physical systems where the extraordinary-log universality class can be observed.

Fermi surface symmetric mass generation and its application in nickelate superconductor
2023-12-08 14:30 - 16:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Joint Quantum Matter in Mathematics and Physics & Topological Quantum Matter Seminar
Speaker: Da-Chuan Lu (UCSD)
Title: Fermi surface symmetric mass generation and its application in nickelate superconductor
Abstract: Symmetric mass generation (SMG) is a novel interaction-driven mechanism that generates fermion mass without breaking symmetry, unlike the standard Anderson-Higgs mechanism. SMG can occur in the fermion system without quantum anomalies. In this talk, I will focus on the SMG for the systems with finite fermion density, i.e., the Fermi surface. I will discuss the Fermi surface anomaly and Fermi surface SMG. Lastly, I will talk about its application in the newly found nickelate superconductors, where the superconductivity emerges without a nearby spontaneous symmetry-breaking phase.

When does a three-dimensions Chern-Simons theory have a time reversal symmetry?
2023-12-14 14:30 - 16:00 | Virtual
Speaker: Roman Geiko (UCLA)
Title: When does a three-dimensions Chern-Simons theory have a time reversal symmetry?
In this talk, I will discuss the time reversal invariance of (spin-) Chern-Simons theory in 3 dimensions at both classical and quantum levels. I will show how to obtain a complete classification of Abelian anyons with the time reversal symmetry expressed in terms of the higher Gauss sums. Then, I will comment on the time reversal symmetry of Chern-Simons in the non-Abelian case.

Exact lattice chiral symmetry in 2d gauge theory
2023-12-15 10:00 - 11:30 | Virtual
Quantum Matter Seminar
Speaker: Aleksey Cherman (UMN)
Title: Exact lattice chiral symmetry in 2d gauge theory
Abstract: Preserving the symmetries of massless fermions is a well-known challenge in lattice field theory. I’ll discuss symmetry-preserving lattice regularizations of 2d QED with one and two flavors of Dirac fermions, as well as the `3450′ chiral gauge theory. The construction leverages bosonization and recently-proposed modifications of Villain-type lattice actions. The internal global symmetries act just as locally on the lattice as they do in the continuum, the anomalies are reproduced at finite lattice spacing, and in each case we’ve found a sign-problem-free dual formulation.

Gauging spacetime inversions
2024-01-26 09:30 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Daniel Harlow (MIT)
Title: Gauging spacetime inversions
Abstract: Spacetime inversion symmetries such as parity and time reversal play a central role in physics, but they are usually treated as global symmetries. In quantum gravity there are no global symmetries, so any spacetime inversion symmetries must be gauge symmetries. In particular this includes CRT symmetry (in even dimensions usually combined with a rotation to become CPT), which in quantum field theory is always a symmetry and seems likely to be a symmetry of quantum gravity as well. I’ll discuss what it means to gauge a spacetime inversion symmetry, and explain some of the more unusual consequences of doing this. In particular I’ll argue that the gauging of CRT is automatically implemented by the sum over topologies in the Euclidean gravity path integral, that in a closed universe the Hilbert space of quantum gravity must be a real vector space, and that in Lorentzian signature manifolds which are not time-orientable must be included as valid configurations of the theory.
