Monday, September 9th, 2024

Workshop: Nathan Seiberg

Time: 9:30 AM - 10:30 AM

Location: SCGP 102

**Title:**Anomalous Continuous Translations**Speaker:**Nathan Seiberg**Abstract:**We will discuss a large class of non-relativistic continuum field theories where the Euclidean symmetry of the classical theory is violated in the quantum theory by an Adler-Bell-Jackiw-like anomaly. In particular, the continuous translation symmetry of the classical theory is broken in the quantum theory to a discrete symmetry. Furthermore, that discrete symmetry is extended by an internal symmetry. We will show that in some cases, the anomalous continuous translation symmetry is resurrected as an exact noninvertible continuous translation symmetry. We will also discuss the relation between this phenomenon and underlying lattice models.
Workshop: Olexei Motrunich

Time: 11:00 AM - 12:00 PM

Location: SCGP 102

**Title:**Fractionalization of Faraday lines in generalized compact quantum electrodynamics models**Speaker:**Olexei Motrunich**Abstract:**Motivated by ideas of fractionalization and topological order in bosonic models with short-range interactions, we consider similar phenomena in formal lattice gauge theory models where basic constituents are quantum lines. In the first example, we show that a compact quantum electrodynamics (CQED) can have, besides familiar Coulomb and confined phases, additional unusual confined phases where excitations are quantum lines carrying fractions of the elementary unit of electric field strength. Specifically, we construct a model that has N-tupled monopole condensation and realizes 1/N fractionalization of the quantum Faraday lines. In the second example, we consider a CQED x boson model in (3+1)D realizing condensation of bound states of d monopoles and c bosons. When d=1, these phases are analogs of bosonic SPT phases for such CQED × boson systems and have quantized cross-transverse response given by the integer c; while when d>1 these phases are analogs of bosonic SET phases and have fractional cross-transverse response given by a rational number c/d and feature fractionalized Faraday line excitations of the CQED and fractionalized boson particle excitations. In the third example, we consider a CQED x CQED model in (4+1)D realizing condensation of bound states of d monopoles (which are quantum lines in four spatial dimensions) and c electric field lines. When d=1, these are SPT phases for such CQED x CQED systems; while for d>1 they are SET phases featuring fractionalized Faraday lines. Such topological phases of CQED systems also show interesting physics at spatial boundaries. This talk is based on PRB 90, 214505 (2014) and PRX 4, 041049 (2014) and unpublished work.**Math Event:**Symplectic Geometry, Gauge Theory, and Low-Dimensional Topology Seminar: Sebastian Haney - Infinity inner products and open Gromov--Witten invariants

Time: 12:30 PM - 1:55 PM

Location: Math 4-130

**Title:**Infinity inner products and open Gromov--Witten invariants**Speaker:**Sebastian Haney [Columbia University]**Abstract:**The open Gromov--Witten (OGW) potential is a function defined on the Maurer--Cartan space of a closed Lagrangian submanifold in a symplectic manifold with values in the Novikov ring. From the values of the OGW potential, one can extract open Gromov--Witten invariants, which count pseudoholomorphic disks with boundary on the Lagrangian. Existing definitions of the OGW potential only allow for the construction of OGW invariants with values in the real or complex numbers. In this talk, we will present a construction of the OGW potential which gives invariants valued in any field of characteristic 0. The main algebraic input for our construction is an infinity inner product, which comes from a proper Calabi--Yau structure on the Fukaya category. If time permits, we will also discuss a partial extension of our results that give OGW invariants valued in fields of positive characteristic, and connections to homological mirror symmetry. View Details
Workshop: Laurens Lootens

Time: 1:15 PM - 2:15 PM

Location: SCGP 102

**Title:**Entanglement and DMRG in the generalised Landau paradigm**Speaker:**Laurens Lootens**Abstract:**Tensor network methods are the state of the art when it comes to simulating strongly correlated quantum lattice models. Besides their numerical prowess, they have also proven to be invaluable tools in the representation theory of generalised symmetries on the lattice. In this talk, we will give an overview of some of these developments for the case of one-dimensional lattice models, and show that understanding the interplay between dualities and gapped phases from an entanglement point of view unlocks more efficient algorithms for finding ground states.
Program: Tomi Ohtsuki

Time: 2:00 PM - 3:30 PM

Location: SCGP 313

**Title:**Localization-delocalization transitions in disordered Hermitian and non-Hermitian systems**Speaker:**Tomi Ohtsuki
Workshop: Sanjay Moudgalya

Time: 2:30 PM - 3:30 PM

Location: SCGP 102

**Title:**Symmetries in Lattice Systems**Speaker:**Sanjay Moudgalya**Abstract:**While the most general symmetries in the continuum are said to form fusion categories, lattice symmetries can be much more general. In this talk, I will discuss a framework for defining non-trivial symmetries in lattice systems in terms of bond and commutant algebras. On-site symmetries with simple group structures can be understood in this way, but this framework also naturally reveals various kinds of discrete and continuous unconventional symmetries with much more general forms. Additionally, it leads to an understanding of the exhaustive set of terms that preserve these symmetries, which can be useful for exploring the physics of systems with these symmetries. Interestingly, all these symmetries can be interpreted as symmetry-broken ground states of local superoperators, particularly in terms of what is now called "strong-to-weak" symmetry breaking, which imposes constraints on their structure. This idea can also be applied to non-invertible symmetries studied in the literature, and I will present a few examples. Finally, when applied to continuous symmetries, this understanding also naturally reveals the hydrodynamic modes associated with the symmetries, which have consequences for the dynamics of such systems.
Workshop: Nathanan Tantivasadakarn

Time: 4:00 PM - 5:00 PM

Location: SCGP 102

**Title:**p-string condensation as gauging a 1-form symmetry**Speaker:**Nathanan Tantivasadakarn**Abstract:**Coupled layered constructions are invaluable for constructing exactly-solvable models for phases of matter. In the study of fracton phases, it has been appreciated that the X-cube model in 3+1D can be realized from such a construction by starting with a stack of 2+1D toric codes and turning on a coupling which condenses a particular composite object called a ``particle-string". I will show that in fact, the particle-string can be thought of as a symmetry defect of a topological 1-form symmetry. By reformulating p-string condensation as the gauging of this symmetry, we uncover a rich gauging web relating the X-cube model to SPT phases protected by a combination of subsystem and higher-form symmetries, subsystem symmetry fractionalization, as well as uncovering non-trivial extensions between subsystem and topological symmetries. Our study emphasizes the importance of topological symmetries in non-topological phases of matter.
Tuesday, September 10th, 2024

Workshop: Sakura Schafer-Nameki

Time: 9:30 AM - 10:30 AM

Location: SCGP 102

**Title:**SymTFT for Phases with Categorical Symmetries**Speaker:**Sakura Schafer-Nameki**Abstract:**We propose and study the implications of a categorical version of the Landau paradigm by exploring gapped phases and second order phase transitions in (1+1)d and (2+1)d with categorical symmetries. The so-called symmetry topological field theory (SymTFT) provides a setting where these phases can be systematically explored. The SymTFT for a d-dimensional theory is a (d+1)-dimensional TFT, whose topological defects encode the symmetries and generalized charges. Studying gapped and gapless boundary conditions for the SymTFT provides a systematic way to characterizing new phases and phase-transitions in the presence of categorical symmetries. Time-premitting, we will discuss lattice realizations of these phases.
Workshop: Meng Cheng

Time: 11:00 AM - 12:00 PM

Location: SCGP 102

**Title:**TBA**Speaker:**Meng Cheng**Abstract:**TBA
Workshop: Sahand Seifnashri

Time: 1:15 PM - 2:15 PM

Location: SCGP 102

**Title:**Gauging non-invertible symmetries on the lattice**Speaker:**Sahand Seifnashri**Abstract:**I will discuss gauging non-invertible symmetries in 1+1d lattice Hamiltonian systems. I first review the gauging of ordinary (possibly non-on-site) invertible symmetries using topological defects and then generalize it to non-invertible symmetries. As a concrete case, I focus on Rep(D8) non-invertible symmetry acting on tensor product Hilbert space of qubits.
Workshop: Theo Johnson-Freyd

Time: 2:30 PM - 3:30 PM

Location: SCGP 102

**Title:**TBA**Speaker:**Theo Johnson-Freyd**Abstract:**TBA
Workshop: Luisa Eck

Time: 4:00 PM - 5:00 PM

Location: SCGP 102

**Title:**Generalizations of Kitaev’s honeycomb model from braided fusion categories**Speaker:**Luisa Eck**Abstract:**Fusion surface models, as introduced by Inamura and Ohmori, extend the concept of anyon chains to 2+1 dimensions, taking fusion 2-categories as their input. In my talk, I will discuss fusion surface models built from braided fusion 1-categories, which conserve commuting plaquette operators and (non-invertible) 1-form symmetries. I will review how Kitaev’s honeycomb model, including the magnetic-field perturbation and twist defects, is unitarily equivalent to the Ising fusion surface model. Honeycomb models constructed from the ZN Tambara-Yamagami category and the Fibonacci category break time-reversal symmetry explicitly, and are promising candidates for realizing chiral topological order. This talk is based on 2408.04006.**Math Event:**Geometry/Topology Seminar: Rondinelle Batista - Rigidity of free boundary minimal disks in mean convex three-manifolds

Time: 4:00 PM - 5:30 PM

Location: Math P-131

**Title:**Rigidity of free boundary minimal disks in mean convex three-manifolds**Speaker:**Rondinelle Batista [Federal University of Piaui]**Abstract:**In this lecture, we present a local rigidity result for free boundary minimal two-disks $Sigma^2$ that locally maximize the modified Hawking mass on a Riemannian three-manifold $M^3$ with a positive lower bound on its scalar curvature and mean convex boundary. Assuming the strict stability of $Sigma^2$, we prove that a neighborhood of it in $M^3$ is isometric to one of the half de Sitter Schwarzschild space. View Details
Wednesday, September 11th, 2024

Workshop: Paul Fendley

Time: 9:30 AM - 10:30 AM

Location: SCGP 102

**Title:**The uses of lattice topological defects**Speaker:**Paul Fendley**Abstract:**I will describe a variety of applications of non-invertible symmetries and dualities. One use is to extend Kramers-Wannier duality to a large class of models, explaining exact degeneracies between non-(conventional) symmetry-related ground states as well as in the low-energy spectrum. Other applications are to critical models: the universal behaviour under Dehn twists gives exact results for scaling dimensions, while gluing a topological defect to a boundary allows universal ratios of the boundary g-factor to be computed exactly on the lattice. I also will outline how terminating defect lines yields fractional-spin conserved currents, seemingly giving a linear method for Baxterization, I.e. finding an integrable model starting with a braided tensor category.
Program: Cenke Xu

Time: 10:00 AM - 11:00 AM

Location: SCGP 313

**Title:**The "Choi-Spin Liquids" in Steady States**Speaker:**Cenke Xu
Program: Antonio Miguel Garcia-Garcia

Time: 11:00 AM - 12:00 PM

Location: SCGP 313

**Title:**The Sachdev-Ye Kitaev model: from quantum gravity to non-hermitian topology**Speaker:**Antonio Miguel Garcia-Garcia
Workshop: Masaki Oshikawa

Time: 11:00 AM - 12:00 PM

Location: SCGP 102

**Title:**Hidden symmetry in SPT phases and duality**Speaker:**Masaki Oshikawa**Abstract:**While the concept of Symmetry-Protected Topological (SPT) phases was first proposed by Gu and Wen in 2009, a prototypical example of SPT phases, Haldane gap phase in integer spin chains, was much earlier and several "topological" features were examined in the 1980s and 1990s. In 1992, Kennedy and Tasaki constructed a non-local unitary transformation on S=1 chains with open ends, that maps between a Z2×Z2 spontaneously symmetry breaking phase and the Haldane gap phase. In this talk, I will review the historical developments and recent revival of the intriguing duality mapping, which can be used to systematically construct numerous SPT phases.
Workshop: Maissam Barkeshli

Time: 1:15 PM - 2:15 PM

Location: SCGP 102

**Title:**Crystalline symmetry and topological phases of matter**Speaker:**Maissam Barkeshli**Abstract:**TBA
Workshop: Weicheng Ye

Time: 2:30 PM - 3:30 PM

Location: SCGP 102

**Title:**Lieb-Schultz-Mattis constraints and anomaly in 2d and 3d**Speaker:**Weicheng Ye**Abstract:**The Lieb-Schultz-Mattis (LSM) constraints play a fundamental role in quantum matter, as they preclude the existence of a unique, gapped, symmetric ground state based solely on certain symmetry-related properties of a system's Hamiltonian. In this talk, I will discuss how to identify anomalies arising from various LSM constraints in two and three dimensions, with a focus on their representation as specific elements in group cohomology. I will also touch on how to extract symmetry action data in low-energy theories, including symmetry fractionalization in (2+1)-dimensional topological orders and (3+1)-dimensional quantum spin ice. This presentation is based on arXiv:2111.12097 and ongoing work with Chunxiao Liu.
Workshop: Carolyn Zhang

Time: 4:00 PM - 5:00 PM

Location: SCGP 102

**Title:**Mixed state topological order and disordered ensembles**Speaker:**Carolyn Zhang**Abstract:**Topological orders in 2+1d are spontaneous symmetry breaking phases of 1-form symmetries. The notion of symmetry is further enriched when we consider mixed state density matrices, where symmetry can be either “strong” or “weak”. In this work, we give an equivalence relation on density matrices, based on finite Renyi-2 Markov length, that naturally leads to different phases labeled by different symmetry breaking patterns of strong and weak 1-form symmetries. We then examine a natural setting for finding such density matrices: disordered ensembles. In particular, we study the toric code with various types of disorder and show that tuning the type and amplitude of disorder tunes through different spontaneous symmetry breaking phases of strong and weak 1-form symmetries.
Thursday, September 12th, 2024

Workshop: Zohar Komargodski

Time: 9:30 AM - 10:30 AM

Location: SCGP 102

**Title:**Applications of topological tools and RG ideas for Defects in condensed matter and in QFT**Speaker:**Zohar Komargodski**Abstract:**We will review recent results and ongoing work on various interesting defects in quantum field theory. We will show new applications for crystal disclinations and symmetry defects and review recent results on the Boson-Kondo problem.
Workshop: Cenke Xu

Time: 11:00 AM - 12:00 PM

Location: SCGP 102

**Title:**Generalized symmetries under weak-measurement and decoherence**Speaker:**Cenke Xu**Abstract:**A pure quantum state can be driven into a mixed state ensemble through processes such as weak-measurement or decoherence. For mixed states, the notion of symmetry is even richer and more intricate than pure quantum systems, as the symmetry can manifest as either "strong" or "weak". We first introduce a quantum field theory formalism that captures the universal long distance physics of measurement and decoherence, then we apply this formalism to systems with zero form and generalized symmetries. We demonstrate that measurement and decoherence can lead to novel phases and phase transitions. For example, we will discuss 3+1-dimensional systems with spontaneous breaking of a U(1) 1-form symmetry, where measurement can induce a phase transition characterized by a line of fixed points and a self-dual structure. We will also discuss decoherence caused by ancilla anyons, where the categorical symmetry (both strong and weak) becomes a guiding principle of the theory.
Workshop: Po-Shen Hsin

Time: 1:15 PM - 2:15 PM

Location: SCGP 102

**Title:**Generalized Symmetries in Quantum Computation**Speaker:**Po-Shen Hsin**Abstract:**Quantum codes describe many interesting quantum phases of matter such as finite group gauge theories and fractons. A rich set of logical operations in quantum codes is provided by emergent symmetries. We investigate higher group generalized symmetries in finite group gauge theories and discover new fault-tolerant logical gates in quantum codes. By gauging generalized symmetries in higher-form symmetry protected topological phases, we discover candidate non-Abelian self-correcting quantum memories that correspond to non-Abelian topological orders without particles.
Workshop: Dominic Else

Time: 2:30 PM - 3:30 PM

Location: SCGP 102

**Title:**Topological Goldstone phases of matter**Speaker:**Dominic Else**Abstract:**When a continuous symmetry G is spontaneously broken, there are associated gapless Goldstone modes. In quantum many-body systems, Goldstone modes can carry "quantum topology" as a manifestation of quantum entanglement, which is reflected in a quantized topological term in the action of the Goldstone modes. This could manifest in, for example, non-trivial quantum numbers of topological defects of the order parameter. In this talk, I will consider in a general setting what determines the quantum topology of the Goldstone modes, in systems with or without a 't Hooft anomaly for the symmetry G.
Workshop: Salvatore Pace

Time: 4:00 PM - 5:00 PM

Location: SCGP 102

**Title:**Spacetime symmetry enriched SymTFT**Speaker:**Salvatore Pace**Abstract:**The Symmetry TFT (SymTFT) is a powerful tool for separating the symmetries of a theory from its dynamics using a topological theory in one higher dimension. In this talk, we discuss an extension of the SymTFT framework to symmetries where internal symmetries have nontrivial interplay with spacetime symmetries using spacetime symmetry-enriched topological orders. Such interplays include, for instance, modulated symmetries and Lieb-Schultz-Mattis (LSM) anomalies. We formulate these spacetime symmetry enriched SymTFTs as (partially) topological Euclidean field theories and quantum codes. Using them, we explore interesting gauging webs with non-invertible modulated symmetries, non-invertible translation symmetries, and LSM anomalies of non-invertible symmetries. We complement this SymTFT analysis by reproducing this gauging web directly in simple 1+1D quantum chains of G-qudits.
Friday, September 13th, 2024

Workshop: Tian Lan (Zoom - Remote)

Time: 9:30 AM - 10:30 AM

Location: SCGP 102

**Title:**Category of SET orders**Speaker:**Tian Lan (ZOOM)**Abstract:**We propose the representation principle to study physical systems with a given symmetry. In the context of symmetry enriched topological orders, we give the appropriate representation category, the category of SET orders. For fusion n-category symmetries, we show that the category of SET orders encodes almost all information about the interplay between symmetry and topological orders, in a natural and canonical way. These information include defects and boundaries of SET orders, symmetry charges, explicit and spontaneous symmetry breaking, stacking of SET orders, gauging of generalized symmetry, as well as quantum currents (SymTFT or symmetry TO). We also provide a detailed categorical algorithm to compute the generalized gauging. In particular, we proved that gauging is always reversible, as a special type of Morita-equivalence. The explicit data for ungauging, the inverse to gauging, is given.
Program: Masatoshi Sato

Time: 10:00 AM - 11:30 AM

Location: SCGP 313

**Title:**Non-Hermitian topological phases (Lecture 2)**Speaker:**Masatoshi Sato
Workshop: Liang Kong

Time: 11:00 AM - 12:00 PM

Location: SCGP 102

**Title:**Higher Condensation Theory**Speaker:**Liang Kong**Abstract:**It was known for more than 20 years that many phase transitions between (topological) quantum phases or (topological) quantum field theories are driven by defect condensations. The only fully established defect condensation theory is the theory of anyon (or boson) condensations in 2+1D topological orders (or TQFTs). Little is known for the condensations of higher dimensional defects in higher dimensional topological orders. In this talk, I will explain a unified mathematical theory of defect condensations in topological orders in all dimensions based on higher categories, higher algebras and higher representations. My talk is based on a recent work arXiv:2403.07813 joint with Zhi-Hao Zhang, Jiaheng Zhao and Hao Zheng.
Workshop: Zheng-Cheng Gu

Time: 1:15 PM - 2:15 PM

Location: SCGP 102

**Title:**Fixed-point tensor network construction for rational conformal field theory**Speaker:**Zheng-Cheng Gu**Abstract:**The novel concept of entanglement renormalization and its corresponding tensor network renormalization technique have been highly successful in developing a controlled real space renormalization group (RG) scheme. In this talk, I will present an explicit analytical construction of the fixed point(FP) tensor for 2D rational CFT. We define it as a correlation function between the "boundary-changing operators" on triangles. Our construction fully captures all the real-space RG conditions. We also provide a concrete example using the Ising model to compute the scaling dimensions explicitly based on the corresponding FP tensor. Interestingly, our construction of FP tensors is closely related to a strange correlator, where the holographic picture naturally emerges. Our results also open a new door towards understanding CFT in higher dimensions.
Workshop: Kansei Inamura

Time: 2:30 PM - 3:30 PM

Location: SCGP 102

**Title:**1+1d SPT phases with non-invertible symmetries: interfaces and parameterized families**Speaker:**Kansei Inamura**Abstract:**Symmetry protected topological (SPT) phases with ordinary group symmetries realize anomalous symmetries on the boundaries. In the first half of this talk, I will generalize this result to 1+1d SPT phases with finite non-invertible symmetries using their tensor network representations. I will show that the symmetry algebra acting on the interface between different SPT phases is anomalous, which leads to degenerate ground states in the presence of the interface. The latter half of this talk discusses parameterized families of 1+1d SPT states with non-invertible symmetries. I will show how to define an invariant of such a family and argue that it can be identified with a generalized Thouless pump, i.e., a charge pump from one interface to another. This talk is based on my recent work with Shuhei Ohyama.
Workshop: Omer Aksoy

Time: 4:00 PM - 5:00 PM

Location: SCGP 102

**Title:**Non-invertible reflections from gauging modulated symmetries**Speaker:**Omer Aksoy**Abstract:**Modulated symmetries are internal symmetries that act non-uniformly in space and are generalizations of, for example, dipole symmetries. Because of their spatial modulation, such symmetries interact non-trivially with spatial symmetries, such as translations or reflections. In this talk, I will describe how finite Abelian modulated symmetries can be gauged in one spatial dimension. In particular, I will demonstrate that, under certain sufficient conditions, after gauging, the dual modulated symmetries are isomorphic to those before gauging. I will explain how Kramers-Wannier-like duality maps arise from this isomorphism and become non-invertible reflection symmetries of generalized transverse field Ising models with modulated symmetries.