Boundary conformal field theory and symmetry protected topological phases in 2+1 dimensions

2017/04/30 by Bo Han, Apoorv Tiwari, Chang-Tse Hsieh +1 · 1 citation
Physics and Astronomy · #cond-mat.str-el #hep-th

paper · pdf · doi:10.1103/physrevb.96.125105

published as Phys. Rev. B 96, 125105 (2017) · 17 pages, 3 figures, Published version

arxiv created 2017/09/10 · arxiv updated 2017/09/13

Abstract

We propose a diagnostic tool for detecting non-trivial symmetry protected topological (SPT) phases protected by a symmetry group G in 2+1 dimensions. Our method is based on directly studying the 1+1-dimensional anomalous edge conformal field theory (CFT) of SPT phases. We claim that if the CFT is the edge theory of an SPT phase, then there must be an obstruction to cutting it open. This obstruction manifests in the in-existence of boundary states that preserves both the conformal symmetry and the global symmetry G. We discuss the relation between edgeability, the ability to find a consistent boundary state, and gappability, the ability to gap out a CFT, in the presence of G. We study several cases including time-reversal symmetric topological insulators, ℤ_N symmetric bosonic SPTs, and ℤ₂ × ℤ₂ symmetric topological superconductors.

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