Quantization of non-Abelian Berry phase for time reversal invariant systems

TL;DR

This paper introduces a quantized non-Abelian Berry phase for time reversal invariant systems, extending the concept to five-dimensional parameter space and revealing its topological quantization and relation to anomalies.

Contribution

It proposes a new five-dimensional integral definition of non-Abelian Berry phase that is quantized and applicable to time reversal invariant systems.

Findings

The non-Abelian Berry phase is quantized into two values.

The five-dimensional integral captures the topological nature of the phase.

The phase relates to nonperturbative anomalies.

Abstract

We present a quantized non-Abelian Berry phase for time reversal invariant systems such as quantum spin Hall effect. Ordinary Berry phase is defined by an integral of Berry's gauge potential along a loop (an integral of the Chern-Simons one-form), whereas we propose that a similar integral but over five dimensional parameter space (an integral of the Chern-Simons five-form) is suitable to define a non-Abelian Berry phase. We study its global topological aspects and show that it is indeed quantized into two values. We also discuss its close relationship with the nonperturbative anomalies.