Emergence in Complex Systems

As realized for the first time in 1980s, quantum many-body systems in reduced spatial dimensions can sometimes undergo a special type of ordering which does not break any symmetry but introduces long-range entanglement and emergent excitations that have radically different properties from their…

Symmetry protected topological (SPT) states are generalizations of topological band insulators to interacting systems. They possess a gapped bulk spectrum together with symmetry protected edge states, with no topological order. There has been recently an intense effort to classify SPT states both in…

In this talk, I will show the emergence of p+ip topological superconducting ground state in infinite-U Hubbard model on honeycomb lattice, from both state-of-art Grassmann tensor-network numerical approach and quantum field theory approach.

Some time ago (1999), Dy2Ti2O7, was shown to be a magnetic analog of water ice, and thus dubbed "spin ice". Recently, theories and experiments have developed the perspective of viewing excitations within the low temperature phase of this spin ice as monopoles. I will present early results of…

Standard picture of a topologically-nontrivial phase of matter is an insulator with a bulk energy gap, but metallic surface states, protected by the bulk gap. Recent work has shown, however, that certain gapless systems may also be topologically nontrivial, in a precise and experimentally observable…

We show that double perovskites with 3d and 5d transition metal ions exhibit spin-orbit coupled magnetic excitations, finding good agreement with neutron scattering experiments in bulk powder samples. Motivated by experimental developments in the field of oxide heterostructures, we also study double…

We developed a general method to compute the correlation functions of FQH states on a curved space. The computation features the gravitational trace anomaly and reveals geometric properties of FQHE. Also we highlight a relation between the gravitational and electromagnetic response functions. The…

I will look at two cases of the interplay of geometry (curvature) and topology: (1) 3D Topological metals: how to understand their surface "Fermi arcs" in terms of their emergent conservation laws and the Streda formula for the non-quantized anomalous Hall effect. (2) The Hall viscosity tensor in…

We demonstrate that the many-body localized phase is characterized by the existence of infinitely many local conservation laws. We argue that many-body eigenstates can be obtained from product states by a sequence of nearly local unitary transformation, and therefore have an area-law entanglement…

In both classical and quantum critical systems, universal contributions to the mutual information and Renyi entropy depend on geometry. I will first explain how in 2d classical critical systems on a rectangle, the mutual information depends on the central charge in a fashion making its numerical…

A 3d electron topological insulator (ETI) is a phase of matter protected by particle-number conservation and time-reversal symmetry. It was previously believed that the surface of an ETI must be gapless unless one of these symmetries is broken. A well-known symmetry-preserving, gapless surface…

Within each of nature's crystals is an exotic quantum world of electrons weaving to and fro. Each crystal has it's own unique tapestry, as varied as the crystals themselves. In some crystals, the electrons weave an orderly quilt. Within others, the electrons are seemingly entwined in an entangled…