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

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

2009-03-18

arxiv.org/abs/0903.3098v1

J.Phys.Soc.Jpn.78:093001,2009

Physics

Condensed Matter

Mesoscale and Nanoscale Physics

5 pages

Scientific paper

10.1143/JPSJ.78.093001

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.

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