ICTS

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.

Exact solutions for excited states in non-integrable quantum Hamiltonians have revealed novel dynamical phenomena that can occur in quantum many-body systems. This work proposes a method to analytically construct a specific set of volume-law-entangled zero-energy exact excited eigenstates in a large class of spin Hamiltonians. In particular, we show that all spin chains that satisfy a simple set of conditions host exact volume-law zero-energy eigenstates in the middle of their spectra. Examples of physically relevant spin chains of this type include the transverse-field Ising model, PXP model, spin-S XY model, and spin-S Kitaev chain. Although these eigenstates are highly atypical in their structure, they are thermal with respect to local observables. Our framework also unifies many recent constructions of volume-law entangled eigenstates in the literature. Finally, we show that a similar construction also generalizes to spin models on graphs in arbitrary dimensions.

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.

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.

I will provide an introduction to generalized symmetries, including higher-form and non-invertible symmetries, from a quantum field theory perspective.

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.

I will provide an introduction to generalized symmetries, including higher-form and non-invertible symmetries, from a quantum field theory perspective.

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.

I give a pedagogical review of the general properties of frustration-free quantum spin systems and fermionic systems and discuss their applications.

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.

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.

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.

In these lectures, I will give an overview of the role of symmetries in the dynamics of quantum many-body systems. I will begin by introducing a rigorous formalism for studying symmetries and their associated quantum-number sectors on a lattice, based on so-called bond and commutant algebras. This framework not only captures conventional on-site symmetries, but also reveals novel types of symmetry that can arise in local systems. Such novel symmetries can lead to unconventional forms of ergodicity breaking, including Hilbert space fragmentation and quantum many-body scars, and I will present concrete examples of systems exhibiting these phenomena. I will also highlight connections between this dynamical perspective on symmetries and the categorical framework commonly used to analyze symmetries in ground-state phases. Finally, I will discuss how continuous symmetries give rise to emergent hydrodynamical behavior, and show how these behaviors can be derived systematically, with concrete illustrations drawn from analytically tractable random quantum circuits.

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.