Exotic quantum holonomy induced by degeneracy hidden in complex parameter space

TL;DR

This paper reveals that exotic quantum holonomies, which involve changes in eigenspaces and eigenvalues during adiabatic evolution, are linked to degeneracies in complex parameter space, specifically exceptional points of non-Hermitian Hamiltonians.

Contribution

The study extends parameter space into complex numbers to connect exotic holonomies with degeneracies of non-Hermitian Hamiltonians, clarifying their origin.

Findings

Exotic holonomies are related to degeneracies in complex parameter space.

Exceptional points explain the characteristics of exotic holonomies.

The work unifies understanding of non-trivial quantum holonomies.

Abstract

An adiabatic change of a bound state along a closed circuit in the parameter space can induces holonomies not only in the phase of the state, but also in the associated eigenspace and eigenvalue. The former is the well-known Berry phase while the latter, namely the exotic holonomy, is found a decade ago and its origin has not been understood yet. By extending the parameter into the complex number, the correspondence of the exotic holonomies and the degeneracy of the non-Hermitian Hamiltonian, or the exceptional points, is revealed. We show that this explains all the known non-trivial characteristics of the exotic holonomies.