Condensed Matter

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.