Exotic quantum holonomy in Hamiltonian systems

TL;DR

This paper investigates how quantum eigenstates can undergo exotic holonomies, exchanging states after cyclic parameter changes, due to non-Abelian gauge potentials, demonstrated through solvable multi-level models.

Contribution

It reveals the occurrence of exotic quantum holonomies caused by non-Abelian gauge potentials in Hamiltonian systems with level crossings, supported by explicit solvable models.

Findings

Exotic holonomies can occur in quantum systems with level crossings.

Non-Abelian gauge potentials induce eigenstate exchanges after cyclic evolutions.

Explicit models demonstrate the theoretical predictions.

Abstract

We study the evolution of quantum eigenstates in the presence of level crossing under adiabatic cyclic change of environmental parameters. We find that exotic holonomies, indicated by exchange of the eigenstates after a single cyclic evolution, can arise from non-Abelian gauge potentials among non-degenerate levels. We illustrate our arguments with solvable two and three level models.