Condensed Matter

The modern conception of phases of matter has undergone tremendous developments since the first observation of topologically ordered states in fractional quantum Hall systems in the 1980s. In this paper, we explore the question: In principle, how much detail of the physics of topological orders can be observed using state of the art technologies? We find that using surprisingly little data, namely the toric code Hamiltonian in the presence of generic disorders and detuning from its exactly solvable point, the modular matrices -- characterizing anyonic statistics that are some of the most fundamental fingerprints of topological orders -- can be reconstructed with very good accuracy solely by experimental means. This is a first experimental realization of these fundamental signatures of a topological order, a test of their robustness against perturbations, and a proof of principle -- that current technologies have attained the precision to identify phases of matter and, as such, probe an extended region of phase space around the soluble point before its breakdown. Given the special role of anyonic statistics in quantum computation, our work promises myriad applications in both probing and realistically harnessing these exotic phases of matter.

We  examine 1D spin-chains evolving under random local unitary circuits and prove a number of exact results on the behavior of out-of-time-ordered commutators (OTOCs), and entanglement growth. These results follow from the observation that the spreading of operators in random circuits is described by a ``hydrodynamical'' equation of motion. In this hydrodynamic picture quantum information travels in a front with a `butterfly velocity' $v_{\text{B}}$ that is smaller than the light cone velocity of the system, while the front itself broadens diffusively in time. The OTOC increases sharply after the arrival of the light cone, but we do \emph{not} observe a prolonged exponential regime of the form $\sim e^{\lambda_\text{L}(t-x/v)}$ for a fixed Lyapunov exponent $\lambda_\text{L}$, in disagreement with the existing QFT literature on OTOCs. We find that the diffusive broadening of the front has important consequences for entanglement growth, leading to an entanglement velocity that can be significantly smaller than the butterfly velocity. We conjecture that the hydrodynamical description applies to more generic ergodic systems and support this with numerical simulations. When the circuits are constrained so as to conserve a U$(1)$ charge, we show that the OTOC acquires a diffusively decaying component. 

Low-energy states of quantum spin liquids are thought to involve partons living in a gauge-field background. We study the spectrum of Majorana fermions of the Kitaev honeycomb model on spherical clusters. The gauge field endows the partons with half-integer orbital angular momenta. As a consequence, the multiplicities do not reflect the point-group symmetries of the cluster, but rather its projective symmetries, operations combining physical and gauge transformations. The projective symmetry group of the ground state is the double cover of the point group.

Two seemingly different quantum field theories may secretly describe the same underlying physics — a phenomenon known as “duality”. Duality has been proved powerful in condensed matter physics, since many difficult questions can be drastically simplified in certain “dual” pictures. This is especially valuable for strongly interacting many-body problems, for which traditional tools (such as perturbation theory) are often not applicable. 

Recent developments on dualities have also revealed deep connections between several previously unrelated topics in modern condensed matter physics, including topological insulators, fractional quantum Hall effects and quantum phase transitions. Connections were also made between dualities in condensed matter physics and in high energy physics. I will give a brief review of some of these developments.

Topological phases of matter entail a prominent research theme, featuring
distinct characteristics that include protected metallic edge states and
the possibility of fractionalized excitations. With the advent of symmetry
protected topological (SPT) phases, many of these phenomena have
effectively become accessible in the form of readily available band
structures. Whereas the role of (anti-)unitary symmetries in such SPT
states has been thoroughly understood, the inclusion of lattice symmetries
provides for an active area of research.

In this talk, I will present a short overview of results on defects in SPT
states that directly motivate the existence of additional physics beyond
the characterization based on (anti-)unitary symmetries. More importantly,
I will then connect these ideas to recent work in which we were able to map
out all different gapped phases of free fermion systems in the presence of
solely lattice symmetries. This revolves around a very simple algorithm
that matches a rather involved mathematical perspective in terms of a
framework called K-theory. I will then discuss the implications of these
combinatorial arguments, such as their impact on the description of Weyl
phases, and sketch related ideas and future perspectives.

Many strongly-correlated systems like high Tc cuprates and heavy fermions have interesting features going beyond quasi-particle description. While Sachdev-Ye-Kitaev(SYK) models are exactly solvable models that can provide a platform to study these physics. In this talk, I will discuss interesting features about the SYK models, including extensive zero temperature entropy and maximally chaos. I will also show some generalization of the SYK models and discuss physical insights from them.

Finite-size spectra and entanglement both characterize nonlocal physics of quantum systems, and are universal properties of a CFT. I discuss the energy spectrum of the Wilson-Fisher CFT on the torus in the \epsilon and 1/N expansions. I also consider a class of deconfined quantum critical points where the torus spectrum contains signatures of proximate Z2 topological order. Finally, I compute the entanglement entropy of the Wilson-Fisher and Gross-Neveu CFTs in the large N limit, where an exact mapping to free field entanglement is obtained. Comparison is made with numerics.