CMSA

Anomalies of (1+1)D categorical symmetries
2023-05-12 10:00 - 11:30 (America/New_York) | 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.

Quantum Circuits to local Hamiltonian: role in quantum complexity and new constructions
2024-02-02 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Anurag Anshu (Harvard)
Title: Quantum Circuits to local Hamiltonian: role in quantum complexity and new constructions
Abstract: At the heart of the theory of NP completeness lies a mapping from classical circuits to constraint satisfaction problems (classical local Hamiltonians).
The quantum analogue of this is the remarkable history state construction of Kitaev (building upon Feynman’s work). This talk will provide an introduction to this mapping and its crucial role in bridging quantum computer science and quantum many-body physics research. Then, we will describe a new mapping using tensor networks and quantum fault tolerance (https://arxiv.org/abs/2309.16475). Time permitting, we will discuss the relevance of this mapping to the quantum PCP conjecture.

Flavor hierarchy from smooth confinement & Towards a complete classification of 6d supergravities
2024-02-06 16:00 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Yuta Hamada (KEK, Tsukuba)
Title: Flavor hierarchy from smooth confinement & Towards a complete classification of 6d supergravities
Abstract: The talk consists of two independent parts. In the first part, I will talk about a new model to explain the Standard Model flavor hierarchy. Our model is based on explicit smooth confinement. The smallness of the first- and second-family fermion masses is explained by the exponential hierarchy via dimensional transmutation. In the second part, I will talk about a classification of 6D supergravities. We make progress towards a complete classification of 6D supergravities with minimal supersymmetry and non-abelian gauge group.
References – arXiv: 2209.15244, 2309.15152, 2311.00868

Quantum Algorithms to Recognize Phases of Matter and Exactly Solvable 2D Models with Anomalous Entanglement Entropy
2024-02-09 09:30 - 11:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Soonwon Choi (MIT)
Title: Quantum Algorithms to Recognize Phases of Matter and Exactly Solvable 2D Models with Anomalous Entanglement Entropy
Abstract: In this talk, I will report my two recent results at the intersection of quantum information and strongly interacting phases of matters.
In the first half of the talk, we describe exact quantum algorithms that recognize a class of 1D gapped phases, namely symmetry protected topological phases or spontaneous symmetry breaking phases protected by abelian internal symmetry. The key idea is to observe the conceptual similarity between renormalization group (RG) flow and error correction, and to implement the latter as unitary circuits emulating the RG flow. Our algorithm guarantees faithful recognition of a target phase with a small number of input quantum state samples.
In the second half, we present a class of 2D Hamiltonians, where the exact ground state wavefunctions can be exactly evaluated and shown to exhibit anomalous entanglement properties. One class of our models exhibit area-law scaling entanglement entropy, but this is mostly due to non-local correlation: one finds that the topological entanglement entropy also scales with the size of subsystem choices. By making simple modifications, we can also devise 2D models with volume-law scaling bipartite entanglement entropy. Our results can be understood as a generation of the 1D Motzkin model to 2D systems.
Based on work done with Ethan Lake and Shankar Balasubramanian
https://arxiv.org/abs/2211.09803
https://arxiv.org/abs/2305.07028

Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
2024-02-14 16:00 - 17:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Sen Hu (Shanghai Institute for Mathematics and Interdisciplinary Study)
Title: Quantum Algebra of Chern-Simons Matrix Model and Large N Limit
Abstract: In this talk we discuss the algebra of quantum observables of the Chern-Simons matrix model which was originally proposed by Susskind and Polychronakos to describe electrons in fractional quantum Hall effects. We establish the commutation relations for its generators and study the large N limit of its representation. We show that the large N limit algebra is isomorphic to the uniform in N algebra studied by Costello, which is conjecturally isomorphic to the deformed double current algebra studied by Guay. Under appropriate scaling limit, we show that the large N limit algebra degenerates to a Lie algebra which admits a surjective map to the affine Lie algebra of u(p). This leads to a complete proof of the large N emergence of the u(p) current algebra as proposed by Dorey, Tong and Turner. This also suggests a rigorous derivation of edge excitation of a fractional quantum Hall droplet. This is a joint work with Si Li, Dongheng Ye and Yehao Zhou (arXiv: 2308.14046).

Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
2024-02-16 10:30 - 12:00 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Susanne Yelin (Harvard)
Title: Programmable Simulations of Molecules and Materials with present-day Reconfigurable Quantum Processors
Abstract: Simulations of quantum chemistry and quantum materials are believed to be among the most important potential applications of quantum information processors, but realizing practical quantum advantage for such problems is challenging. We introduce a simulation framework for strongly correlated quantum systems that can be represented by model spin Hamiltonians. Our approach leverages reconfigurable qubit architectures to programmably simulate real-time dynamics and introduces an algorithm for extracting chemically relevant spectral properties via classical co-processing of quantum measurement results. We develop a digital-analog simulation toolbox for efficient Hamiltonian time evolution utilizing digital Floquet engineering and hardware-optimized multi-qubit operations to accurately realize complex spin-spin interactions, and as an example present an implementation proposal based on Rydberg atom arrays. Then, we show how detailed spectral and other relevant chemical information can be extracted from these dynamics through snapshot measurements and single-ancilla control, enabling the evaluation of excitation energies and finite-temperature susceptibilities from a single-dataset. To illustrate the approach, we show how this method can be used to compute key properties of a polynuclear transition-metal catalyst and 2D magnetic materials.

Spontaneously Broken (-1)-form symmetries
2024-02-23 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Motoo Suzuki (Harvard)
Title: Spontaneously Broken (-1)-form symmetries
Abstract: Spontaneous breaking of symmetries leads to universal phenomena. We extend this notion to (−1)-form U(1) symmetries. The spontaneous breaking is diagnosed by a dependence of the vacuum energy on a constant background field θ, which can be probed by the topological susceptibility. This leads to a reinterpretation of the Strong CP problem as arising from a spontaneously broken instantonic symmetry in QCD. We discuss how known solutions to the problem are unified in this framework and explore some, so far unsuccessful, attempts to find new solutions. I will also talk about our ongoing work on the explicit breaking by monopoles.

A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
2024-03-08 09:00 - 10:00 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Semeon Valgushev (Iowa State University)
Title: A model for studying the sign problem on quantum computers: Z(3) gauge theory with three fermion flavors in 1+1 dimensions
Abstract: Many properties of quantum field theories can be understood with the help of classical numerical methods. Yet there are several outstanding problems — most remarkably the behaviour of nuclear matter at finite density and out-of-equilibrium real-time dynamics — that require the use of quantum algorithms. We present a simple yet physically rich toy model of QCD/nuclear matter at finite density, termed “QZD”, where Z stands for Z(3) gauge theory coupled to Nf = 3 fermion flavors, suitable for simulation on near-term quantum devices. We study it using tensor networks and find that in weak coupling the spectrum is that of the expected mesons and baryons, although the corrections in weak coupling are nontrivial. In strong coupling, besides the usual baryon, the singlet meson is a baryon anti-baryon state. For two special values of the coupling constant, the lightest baryon is degenerate with the lightest octet meson, and the lightest singlet meson, respectively.

Cluster state as a noninvertible SPT phase
2024-03-13 10:00 - 12:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Shu-Heng Shao (SUNY Stony Brook)
Title: Cluster state as a noninvertible SPT phase

Abstract: We will point out a non-invertible symmetry of the ordinary 1+1d Z2xZ2 cluster Hamiltonian. Therefore, the cluster state can be viewed as a non-invertible SPT phase under this fusion category symmetry, which is Rep(D8). We furthermore find two new stabilizer states that are distinct from the cluster state as Rep(D8) SPT phases, but identical as Z2xZ2 SPT phases. Finally, we discuss the degenerate edge modes at the interfaces between these three Rep(D8) SPT phases.

Monopoles, scattering, generalized symmetries
2024-03-15 10:00 - 11:30 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Diego Delmastro (Simons Center for Geometry and Physics)
Title: Monopoles, scattering, generalized symmetries

Abstract: Gauge theory is a very mature subject by now. Surprisingly, some of its symmetries have only been properly understood in the last couple of years. Specifically, such theories typically have a very rich set of symmetries, involving modern notions such as higher-form symmetries, higher-group symmetries, and categorical symmetries. A proper understanding of these generalized symmetries is not really crucial if we are interested in scattering processes involvingfundamental particles only, but it does become quite essential if we want to add monopoles into the mix. In this talk I will review where these generalized symmetries come from, and how they impose constraints on scattering amplitudes of elementary particles against heavy monopoles. This will allow us to resolve a decades-old puzzle concerning such processes, where incoming electrons appear to become fractional particles after the scattering event.

Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem
2024-03-22 09:00 - 10:30 | Virtual
Quantum Matter in Mathematics and Physics Seminar
Speaker: Sungwoo Hong, Korea Advanced Institute of Science and Technology (KAIST)
Title: Non-Invertible Peccei-Quinn Symmetry and the Massless Quark Solution to the Strong CP Problem
Abstract: In this talk, I will discuss a new solution to the strong CP problem, one of the most important and challenging problems, of the Standard Model (SM) based on the generalized global symmetry. To this end, I will first show that there exist non-invertible chiral symmetries acting on quark fields once the SM is extended with gauged quark flavor symmetry. Interestingly enough, such symmetries, which we named them as “non-invertible Peccei-Quinn symmetries”, exist only because the SM has the same number of generations as colors, yet another feature that deserves a fundamental explanation. Then I discuss how these new generalized symmetries set the down Yukawa to be exactly zero and lead to a massless quark solution to the strong CP problem. Completion of the solution requires (i) generation of down quark Yukawas to be consistent with both observed quark mass spectrum and mixings and (ii) generation of O(1) CP violating phase called CKM phase, crucially without destabilizing our solution to the strong CP problem. I will discuss that these rather non-trivial tasks can be achieved by a UV completion in an SU(9) quark color-flavor unification.

Discrete geometry and the modular bootstrap
2024-04-05 10:00 - 11:30 | CMSA Room G10, CMSA, 20 Garden Street, Cambridge, MA, 02138, United States
Quantum Matter in Mathematics and Physics Seminar
Speaker: Henry Cohn (MIT and Microsoft)
Title: Discrete geometry and the modular bootstrap
Abstract: In this talk, I’ll discuss the remarkable connections between the modular bootstrap and sphere packing or ground state problems discovered by Hartman, Mazáč, and Rastelli in 2019, with a focus on opportunities for further progress.
