Quantum anomalies in symmetry-protected topological phases

by Dr Shinsei Ryu (University of Illinois)

Monday 6 Jul 2015, 13:30 → 14:30 Asia/Tokyo

Nishina Hall (RIKEN Wako)

Date: Jul 06 (Mon) Time: 13:30 - Place: Nishina Hall Speaker: Shinsei Ryu (University of Illinois) Title: Quantum anomalies in symmetry-protected topological phases Abstract: Since the discovery of the quantum Hall effect, the notion of topological phases of matter has been extended to those that are well-defined (or: ”protected”) in the presence of a certain set of symmetries, the so-called symmetry-protected topological phases. Their primary examples include, but not limited to, topological insulators and superconductors. Compared to genuine topological phases, symmetry-protected topological phases are more fragile and less entangled states of matter. Hence for their characterization we need to sharpen our understanding on how topological properties of the systems manifest themselves --- in particular in the form of a quantum anomaly.
In this talk, I will discuss our diagnostic scheme to identify topological non-triviality of symmetry protected topological phases, which consisting of “twisting” by symmetries relevant to topological phases, i.e., twisting boundary conditions by symmetries protecting topological phases. This scheme is a proper generalization of Laughlin’s thought experiment in the quantum Hall effect to a wider range of topological phases protected by symmetries. In particular, it can be used to diagnose the stability of non-interacting symmetry-protected topological phases against interactions and disorder. See more QHP seminars