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

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.

5 pages

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Cited by in corpus (3)

• The Euler Number of Bloch States Manifold and the Quantum Phases in Gapped Fermionic Systems
• Quantum distance and the Euler number index of the Bloch band in a 1D spin model
• A new Berry phase term in parity-time symmetric non-Hermitian spin-1/2 quantum systems