Optimal Topological Test for Degeneracies of Real Hamiltonians

Abstract

We consider adiabatic transport of eigenstates of real Hamiltonians around loops in parameter space. It is demonstrated that loops that map to nontrivial loops in the space of eigenbases must encircle degeneracies. Examples from Jahn-Teller theory are presented to illustrate the test. We show furthermore that the proposed test is optimal.

arXiv commentMinor corrections, accepted in Phys. Rev. Lett

References in corpus (4)

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• Geometric Phases and Multiple Degeneracies in Harmonic Resonators
• Topological Phases near a Triple Degeneracy
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