Video Library

In quantum systems with symmetry, the same topological phase can be enriched by symmetry in different ways, resulting in different symmetry transformations of the superselection sectors in the phase. However, not all symmetry transformations are allowed on the superselection sectors in topological phases in purely 2D systems. In this talk, I will discuss some examples of such symmetry enrichment of topological phases, which seem to be consistent with the fusion and braiding rules of the superselection sectors in the theory but are nonetheless impossible to realize in 2D.

I will discuss a family of solvable 3D lattice models that have a ``trivial" bulk, in which all excitations are confined, but exhibit topologically ordered surface states.  I will discuss perturbations to these models that can drive a phase transition in which some of these excitations become deconfined, driving the system into a phase with bulk topological order.

Recently, many new types of bosonic symmetry-protected topological phases, including bosonic topological insulators, were predicted using group cohomology theory.  The bosonic topological insulators have  both  U(1) symmetry (particle number conservation) and time-reversal symmetry, described by symmetry group $U(1)\rtimes Z_2^T$.  In this paper, we propose a projective construction of three-dimensional correlated gapped bosonic state with $U(1)\rtimes Z_2^T$ symmetry.  The gapped bosonic insulator is formed by eight kinds of charge-1 bosons.

The existence of three generations of neutrinos and their mass mixing is a deep mystery of our universe. On the other hand, Majorana's elegant work on the real solution of Dirac equation predicted the existence of Majorana particles in our nature, unfortunately, these Majorana particles have never been observed. In this talk, I will begin with a simple 1D condensed matter model which realizes a T^2=-1 time reversal symmetry protected superconductors and then discuss the physical property of its boundary Majorana zero modes.