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.

Minor corrections, accepted in Phys. Rev. Lett

Cited by in corpus (6)

• Geometry of quantum phase transitions
• Multi-gap topology and non-Abelian braiding of phonons from first principles
• Geometric phases and criticality in spin systems
• Andreev reflection in Euler materials
• Coexisting Euler and Stiefel-Whitney Topological Phases in Elastic Metamaterials
• High-chirality and multiquaternion Weyl nodes in hexagonal ReO${}_3$