Monday, 05 January 2026
The chiral anomalous U(1) symmetry in QCD is expected to play a crucial role in deciding the symmetries and the order of the chiral phase transition. Even in QCD with physical quarks, the two flavor chiral symmetry is fairly well respected. In this talk I will discuss about the role of anomalous U(1) near the chiral (crossover) transition in QCD with physical quarks. I will also discuss how we can understand its temperature dependence from a microscopic description in terms of the eigenvalues and eigenvectors of the QCD Dirac operator and what new insights we have gained in the recent years.
Tuesday, 06 January 2026
The Ising-Higgs model is a paradigmatic example of phases and phase transitions that transcend the standard Landau-Ginzburg-Wilson framework. We investigate exotic critical phenomena along its self-dual line, focusing on two distinct regimes: the "even" vacuum sector and the "odd" finite-anyon-density sector. In the even sector, we employ a machine learning technique based on real-space mutual information optimization to demonstrate that the Higgs-confinement multicritical point lacks a conserved current operator. This finding challenges conjectures proposing an emergent U(1) symmetry at the intersection of Ising* critical lines. In the odd sector, the Higgs and confinement transitions become fundamentally intertwined with valence-bond-solid (VBS) order due to geometric frustration, leading to an intersection of U(1)* critical lines. Our DMRG simulations reveal a simultaneous transition involving Higgs-confinement physics, self-duality breaking, and VBS ordering. Notably, the VBS order exhibits a cascade of incommensurate patterns with progressively increasing length scales before ultimately giving way to a quantum paramagnet. If time permits, I will discuss deconfined criticality in Ising-fermion systems, where confinement and dimerization occur in tandem.
Wednesday, 07 January 2026
I will provide an introduction to fusion categories and explain the extra ingredients needed to describe anyon systems.
We study the magnetic response of flat bands in 2D and show that singular flat bands host anomalous Landau levels that violate Onsager quantization. Under inhomogeneous fluxes, these Landau levels can collapse and reorganize into a disorder-robust, highly degenerate zero-mode manifold at special flux configurations. We demonstrate that an emergent lattice supersymmetry is at play to produce degenerate flat bands in the Hofstadter spectrum and gives rise to partial Aharonov-Bohm caging.
Thursday, 08 January 2026
Plaquette excitations in 2D lattice gauge theories with a finite gauge group G have been known, since at least the works by Bais and de Wild Propitius in the nineties, to behave as non-Abelian anyons carrying localized generalized magnetic fluxes. These plaquette excitations also form one subset of elementary excitations for the famous Kitaev quantum double (KQD) model based on the group G. The other subset corresponds to localized vertex excitations carrying generalized electric charges. Building on recent works by A. Ritz-Zwilling, S. Simon, J.-N. Fuchs and J. Vidal on the exact computation of the partition function of string net models on a surface of arbitrary genus, I will show how to count the degeneracy of an energy eigenspace for the KQD model based on G, with prescribed types of plaquette and site excitations. This formula has the expected form for an emerging topological field theory, based on the modular tensor category obtained by applying the Drinfeld center construction to the category of G-graded vector spaces.
The presence of non-trivial families of quantum states such as charge pumps indiates that a single phase of matter has non-trivial topology. In this talk, based on upcoming work with Sashank Reddy and Nick Jones, I will show that this can be physically detected through higher Berry phases and and visualized in the form of topological textures in the phase diagram. For free fermions, these can be calculated using integrals of Chern-Simons forms of the Bloch-Berry connection and for interacting systems, using field theory. I will also show that bulk-boundary correspondence results in edge modes of the kind not observed in topological phases.
Friday, 09 January 2026
I will provide an introduction to generalized symmetries, including higher-form and non-invertible symmetries, from a quantum field theory perspective.
I will discuss tensor network representations of generalized / categorical symmetries and their intertwining dualities , relate those symmetries to the entanglement spectra of quantum spin systems, and end with a lattice perspective on the generalized Landau paradigm.
Defects are always present in solid state materials. I will present our group’s recent theoretical results showing how quantum-entangled or topological systems can enable local defects to produce surprising global effects. First, in the Kitaev honeycomb quantum spin liquid (QSL), non-magnetic “Stone-Wales” crystallographic defects become imbued with a fluctuating magnetic chirality. The emergent Ising model for their chiralities is ferromagnetic and long ranged (~1/r^2.7), producing an instability to a topological chiral QSL at a finite critical temperature set by the defect density. Second, in the 1/3 magnetization plateau of triangular lattice magnet KCSO, IR spectroscopy observed unusual satellite lines. We show that though these lines are sharp, they arise from disorder and enable its characterization as dilute vacancies. Third, in the Dirac cones of the honeycomb lattice, magnetic impurities induce circulating currents with an associated topological Chern number. Surprisingly, for isolated impurities this induced magnetization and topology is reversed above a critical impurity strength, with a global phase transition generated by the local defect physics.
Quantum condensed matter has traditionally focused on ground states and equilibrium properties of spatially extended systems, such as electrons in crystalline materials. However, the advent of noisy-intermediate-scale-quantum (NISQ) devices has sparked interest in many-body open quantum systems, where condensed matter meets quantum information. In this talk, I will discuss recent progress in defining phases of matter in open quantum systems and present a partial classification of “intrinsically” mixed-state topological order. I will also discuss an autonomous error correction protocol that leverages erasure errors to stabilise a topological quantum memory in two spatial dimensions, which has been a long-standing quest in the field.
Monday, 12 January 2026
I will provide an introduction to generalized symmetries, including higher-form and non-invertible symmetries, from a quantum field theory perspective.
I will discuss tensor network representations of generalized / categorical symmetries and their intertwining dualities , relate those symmetries to the entanglement spectra of quantum spin systems, and end with a lattice perspective on the generalized Landau paradigm.
We identify a three-dimensional system that exhibits long-range entanglement at sufficiently small but nonzero temperature—it therefore constitutes a quantum topological order at finite temperature, the first known example of such order in physically realistic dimensions. The model of interest is known as the fermionic toric code, a variant of the usual 3D toric code, which admits emergent fermionic pointlike excitations. The fermionic toric code, importantly, possesses an anomalous two-form symmetry, associated with the spacelike Wilson loops of the fermionic excitations. We argue that it is this symmetry that imbues low-temperature thermal states with a novel topological order and long-range entanglement. Interestingly, the classification of three-dimensional topological orders suggests that the low-temperature thermal states of the fermionic toric code belong to a phase of matter that, in the context of equilibrium phases of matter, only exists at nonzero temperatures. Relatedly, despite its long-range quantum entanglement, the system only exhibits a classical memory.
Tuesday, 13 January 2026
I give a pedagogical review of the general properties of frustration-free quantum spin systems and fermionic systems and discuss their applications.
In these lectures I will describe the generalized Landau paradigm, which extends the conventional symmetry-breaking framework based on group-like (0-form) symmetries to include generalized symmetries. This perspective organizes the landscape of beyond-Landau phases, including topological phases, through their symmetry structure, and enables the discovery and characterization of many genuinely new phases. I will present the Symmetry Topological Field Theory (SymTFT) as a unifying framework that systematizes the spectrum of generalized charges (representations of generalized symmetries), provides a complete classification of gapped phases with a given symmetry, and offers significant insight into gapless phases and phase transitions. I will also outline how SymTFT data can be translated into concrete lattice Hamiltonians. The lectures will focus on 2+1-dimensional quantum systems with finite internal generalized symmetries, mathematically described by 2-fusion categories.
In this talk, I will show that electrons in the lowest Landau level limit of FQH enjoy the so-called area-persevering diffeomorphism symmetry. This symmetry is the long-wavelength limit of the W-infinity symmetry. The area-preserving diff is a non-abelian higher-rank gauge theory whose linearized version is the traceless symmetric tensor gauge theory. As a consequence of the symmetry, the electric dipole moment and the trace of the quadrupole moment are conserved on a flat background, which demonstrates the fractonic behaviors of FQH excitations. I will derive the renowned Girvin-MacDonald-Platzman (GMP) algebra and the topological Wen-Zee term using the are-preserving diff symmetry.
Wednesday, 14 January 2026
In two dimensions, the scaling theory of localization predicts Anderson localization of disordered, non-interacting fermions lacking any inherent anti-unitary symmetries, independent of microscopic details. In contrast, the presence of charge conjugation symmetry in Class D superconductors enables a richer phase structure, including distinct topological and trivial localized phases, as well as, in specific scenarios, a disorder-driven thermal metal phase. However, this is not generic and depends on the microscopic model, including the nature of disorder. In this work, I will discuss our results on the effects of geometric disorders, such as random bond dilution in such systems. In particular, one finds a broad metallic phase which is realized when the broken links are weakly stitched via concomitant insertion of π fluxes in the plaquettes. I will try to show that it is the interplay of symmetries, underlying topological character and geometrical disorder which lead to such a metal.
Thursday, 15 January 2026
Hilbert space fragmentation has been extensively studied in recent years as it is one of the ways in which a quantum many-body system may evade thermalization. We will discuss some models where kinetic constraints in the Hamiltonian lead to a shattering of the Hilbert space into a large number of disconnected fragments. The Hilbert space fragmentation may be strong or weak depending on the ratio of the size of the largest fragment to the size of the full Hilbert space. Each fragment can be characterized in terms of a single irreducible string (IS), such that all the states of that fragment can be reached via the Hamiltonian starting from the IS. The number of states in a fragment can be obtained from the structure of the IS. The nature of the dynamics can be completely different in different fragments, being non-integrable in some fragments and integrable or even trivial in others. The different behaviors can be understood by studying a variety of quantities, such as the energy level spacing statistics, a plot of the half-chain entanglement versus the energy, the time-evolution of autocorrelation functions, and the Loschmidt echo. We will illustrate all these ideas using some one-dimensional lattice models with density-dependent hopping amplitudes between nearest-neighbor sites.
Friday, 16 January 2026
The Kramers-Wannier (KW) self-duality symmetry of the critical 1D quantum Ising model is the paradigmatic example of a non-invertible symmetry on the lattice. In the infrared (IR) limit, it flows to the Z_2 Tambara-Yamagami fusion category symmetry of the Ising CFT. Most known constructions of such self-dualities arise from gauging Abelian symmetries, including higher-form and subsystem. In this talk, we generalize these constructions by constructing 1D quantum lattice models that we dub "Hopf Ising models". Based on finite-dimensional semisimple Hopf algebras H and defined on a tensor product Hilbert space of Hopf qudits, these models enjoy an "onsite" Rep(H) symmetry. Their Hamiltonians and symmetry operators admit an intuitive diagrammatic form using a non-(co)commutative version of ZX-Calculus. When H is self-dual, we construct a Hopf KW symmetry which emerges at a self-dual coupling separating the paramagnetic and ferromagnetic phases. This enlarged symmetry mixes with lattice translation and, in the IR, flows to a weakly integral fusion category given by a Z_2 extension of Rep(H). We illustrate these ideas with the Kac-Paljutkin algebra H_8, writing down some simple Hamiltonians exhibiting the H_8 KW symmetry and numerically exploring their phase diagram.
The past decade has witnessed spectacular progress in the classification of gapped phases of systems with many quantum degrees of freedom. The long-wavelength description of such phases typically uses quantum field theory with fields placed on a manifold. Motivated by recent advances in quantum technologies that enable the creation of synthetic systems, we define and explore physics in arenas that do not tessellate a manifold, and hence do not yield to conventional quantum field theories on a manifold. The simplest such arenas are made from tree graphs. After introducing these arenas, I will discuss the physics of free fermions on such arenas and demonstrate several new features in the nature of phase transitions. I will then turn to more exotic topologically ordered (long-range entangled phases) in these systems. Highlight results include the demonstration that even the simplest gauge theory in these arenas is fractonic, and a result on the classification of such phases.