Physics (Internal)

Defects in Topologically Ordered Quantum Matter

This event is part of the HET Seminar Series.

Abstract: Topologically ordered states are quantum states of matter with various exotic properties such as topological ground state degeneracies, and quasiparticles with fractional quantum numbers and fractional statistics. At long wavelengths, these are described by topological quantum field theories (TQFTs). In this talk, I will describe a new aspect of topologically ordered states---the twist defects. Twist defects are extrinsic point defects in a topologically ordered state that couple to its topological properties. A simple example includes the end-points of a branch cut in a bilayer system, around which the two layers are exchanged. Such defects, named ``genons", turn out to have rich topological properties and may be realizable in several physical systems. The concept of genons and twist defects thus provides a new direction in the study of topological states of matter and topological quantum computation. In this talk I will first review the basic properties of genons and more general twist defects, and discuss recent proposals of realizing genons in fractional Chern insulators (i.e. lattice fractional quantum Hall states) and conventional bilayer quantum Hall states. I will also provide a unified description of the most generic topological defects in Abelian topological states.