Condensed Matter

Recent years new concepts of symmetries have been developed such as higher form symmetries, and categorical symmetries. The higher form symmetries can be either explicit in a Hamiltonian, or inexplicit as a dual of an ordinary symmetry. The behavior of higher form symmetries are easy to evaluate in phases with gaps. But at quantum criticalities their behaviors are more nontrivial. We evaluate the behaviors of higher form symmetries (either explicit or inexplicit) at various quantum critical points, and demonstrate that for many quantum critical points a universal logarithmic contribution arises, which is analogous to the quantum entanglement entropy. This logarithmic contribution is related to the universal conductance at the quantum critical points, and in some cases can be computed exactly using duality between CFTs developed in last few years. We also evaluate the behavior of categorical symmetries for more exotic cases with subsystem symmetries.

The entanglement pattern of a quantum many-body system can be characterized by quasiparticles and emergent gauge fields, much like those found in Maxwell's theory. My talk begins with the basic aspects of symmetry fractionalization and emergent gauge fields in strongly correlated systems. I will further extend this paradigm into a new type of quantum many-body state, dubbed "fracton phase," from a quantum melting transition of plaquette paramagnetic crystals. These exotic states contain fractionalized sub-dimensional quasiparticles with constraint motion and emergent higher-rank gauge fields. Such constraint dynamics of the quasiparticles bring about an intriguing Bose metal phase with quasi-long range order and yields non-local quantum entanglement. In particular, the key peculiarities of this phase is the UV/IR mixing, where the short wavelength physics controls the low energy theory and hence challenges the standard notion of the renormalization group perspective.

Metals are ubiquitous in nature. One would like to determine the effective field theory that describe the low-energy physics of a metal. Many materials are successfully described by the so-called "Fermi liquid theory", but there is also much interest in "non-Fermi liquid metals" that evade such a description.

In this talk, I will present a very general perspective on metals that strongly constrains the possible effective field theories. The discussion is based on powerful theoretical concepts such as emergent symmetries and anomalies. From this perspective, combined with experimental observations, one can derive strong and unexpected conclusions about the nature of a particular kind of non-Fermi liquid metal, the "strange metal" observed in doped cuprates.

A many-body quantum system that is continually monitored by an external observer may be in distinct dynamical phases, depending on whether or not the observer’s repeated local measurements prevent the buildup of long-range entanglement. The universal properties of the “measurement phase transitions” between these phases remain a challenge. In this talk I will describe new theoretical approaches to measurement phase transitions, making connections with problems in statistical mechanics such as disordered magnets and travelling waves. I will show that exact results are possible in some regimes, including for quantum circuits with all-to-all interactions. (Based on arxiv:2009.11311)

Monitored quantum dynamics has attracted much research attention recently. Environmental monitoring typically leads to the decoherence of a quantum system. We explore the effect of energy-level decoherence in quench dynamics. In particular, we consider the linear quench across quantum critical phase transitions under the influence of decoherence. Due to the critical slowing down, the system will necessarily fall out of equilibrium in the vicinity of the critical point within a time scale known as the freeze-out time. The freeze-out time will scale with the quench rate following the Kibble-Zurek scaling. In the presence of decoherence, we found a new scaling behavior differed from the Kibble-Zurek scaling. We demonstrated our findings in the critical quench between 2D Chern insulator and trivial insulator. We show that the new scaling behavior can be justified from the behavior of Hall conductivity across the quantum quench.

Quantum circuits, relevant for quantum computing applications, present a new kind of many-body problem. Recently it was discovered that the quantum state evolved by random unitary gates, interrupted by occasional local measurements undergoes a phase transition from a highly entangled (volume law) state at small measurement rate to an area law state above a critical rate. I will review the current understanding of this transition from the statistical mechanics and the information perspectives. I will then argue that a circuit with intrinsic symmetries admits more phases, which represent distinct patterns of protection and flow of quantum information. These states can be studied and classified by mapping to an effective ground state problem of a Hamiltonian with enlarged effective symmetry. I will give two simple examples to illustrate these ideas: (i) a circuit with intrinsic Z2 spin symmetry; (ii) A circuit with Gaussian Majorana fermion gates showing a surprising Kosterlitz-Thouless transition in the entanglement content.

This talk starts by reviewing known examples of how topological materials generate new kinds of electrodynamic couplings and effects.  Three-dimensional topological insulators realize a particular electromagnetic coupling known as “axion electrodynamics”, and understanding this leads to an improved understanding of magnetoelectricity in all materials.  We then turn to how topological Weyl and Dirac semimetals can show unique electromagnetic responses; we argue that in linear response the main observable effect solves an old problem via the orbital moment of Bloch electrons, and how in nonlinear optics there should be a new quantized effect, which may have been seen experimentally.  This nonlinear effect has a natural quantum e^3/h^2 and appears in chiral Weyl semimetals over a finite range of frequencies.  We discuss interaction and disorder corrections to nonlinear responses in closing.

Quantum entanglement of pure states has led to new insights into a wide variety of topics. Entanglement of mixed states is however less well understood. In this talk I will focus on a few themes where mixed-state entanglement leads to new insights that are difficult to obtain otherwise. I will mainly focus on two topics: (i) Characterizing finite-temperature topological order (ii) Detecting presence/absence of quasiparticles. Time permitting, I will also discuss a relation between mixed-state entanglement and information obtained from projective measurements, and its application to characterizing multi-component systems, such as quantum disentangled liquids and Kondo lattice systems.

Flat bands in Moire superlattices are emerging as a fascinating new playground for correlated electron physics. I will present the results of several studies inspired by these developments. First, I will address the question of whether superconductivity is possible even in the limit of a perfectly flat band. Then, I will discuss transport properties of a spin-polarized superconductor in the limit of zero spin-orbit coupling, where the topological structure of the order parameter space allows for a new dissipation mechanism not known from conventional superconductors. If time allows, I will also discuss the interpretation of new measurements of the electronic compressibility in twisted bilayer graphene, indicating a cascade of symmetry-breaking transitions as a function of the density of carriers in the system. 

References:

https://arxiv.org/abs/2006.10073

https://arxiv.org/abs/1912.08848

https://arxiv.org/abs/1912.06150

High-temperature superconductivity in the cuprates remains an unsolved problem because the cuprates start off their lives as Mott insulators in which no organizing principle such a Fermi surface can be invoked to treat  the electron interactions.  Consequently, it would be advantageous to solve even a toy model that exhibits both Mottness and superconductivity.  In 1992 Hatsugai and Khomoto wrote down a momentum-space model for a Mott insulator which is safe to say was largely overlooked, their paper garnering just 21 citations (6 due to our group).  I will show exactly[1] that this model when appended with a weak pairing interaction exhibits not only the analogue of Cooper's instability but also a superconducting ground state, thereby demonstrating that a model for a doped Mott insulator can exhibit superconductivity.  The properties of the superconducting state differ drastically from that of the standard BCS theory.  The elementary excitations of this superconductor are not linear combinations of particle and hole states but rather are superpositions of doublons and holons, composite excitations signaling that the superconducting ground state of the doped Mott insulator inherits the non-Fermi liquid character of the normal state.

Additional unexpected features of this model are that it exhibits a superconductivity-induced transfer of spectral weight from high to low energies and a suppression of the superfluid density as seen in the cuprates.

[1] https://www.nature.com/articles/s41567-020-0988-4.

The remarkable experimental advances made it possible to create highly tunable quantum systems of ultracold atoms and trapped ions. These platforms proved to be uniquely suited for probing non-equilibrium behavior of interacting quantum systems. From statistical mechanics, we expect that a non-equilibrium system will thermalize, settling to a state of thermodynamic equilibrium. Surprisingly, there are classes of systems which do not follow this expectation. I will give examples of systems which avoid thermalization, thanks to disorder-induced localization and quantum scarring. While thermalization leads to “scrambling” of quantum information, its absence may protect local quantum coherence. This enables non-equilibrium states of matter not envisioned within the framework of statistical mechanics. I will highlight the recent theoretical insights into the remarkable physical properties of such states, based on the underlying patterns of quantum entanglement. I will finally describe a possible theoretical route towards developing a classification of dynamical universality classes in many-body systems.

We discuss the dynamics of (Rényi) mutual information, logarithmic negativity, and (Rényi) reflected entropy after exciting the ground state by a local operator in (1+1)d conformal field theories. In particular, we contrast "integrable" and "chaotic" conformal field theories, by looking at the quasi-particle picture and its possible breakdown. In comparing the calculations in the two classes of theories, we are able to identify the dynamical mechanism for the breakdown of the quasi-particle picture in 2D conformal field theories. Intriguingly, we also find preliminary evidence that our general lessons apply to quantum systems considerably distinct from conformal field theories, such as integrable and chaotic spin chains, suggesting a  universality of entanglement dynamics in non-equilibrium systems.