Partition Functions and Stability Criteria of Topological Insulators

TL;DR

This paper explores the partition functions of topological insulators, linking their stability to anomalies and modular invariance, and extends the $ ext{Z}_2$ classification to complex interacting systems.

Contribution

It introduces a novel analysis of topological insulator stability using partition functions and extends the $ ext{Z}_2$ classification to non-Abelian and interacting edge states.

Findings

Partition functions reveal stability criteria for topological phases.

Discrete anomalies relate to the lack of modular invariance.

Extended $ ext{Z}_2$ classification to non-Abelian systems.

Abstract

The non-chiral edge excitations of quantum spin Hall systems and topological insulators are described by means of their partition function. The stability of topological phases protected by time-reversal symmetry is rediscussed in this context and put in relation with the existence of discrete anomalies and the lack of modular invariance of the partition function. The $\Z_2$ characterization of stable topological insulators is extended to systems with interacting and non-Abelian edge excitations.