Evidence for Exceptional Points as Topological Defects

TL;DR

This paper reveals that exceptional points in quantum systems act as topological defects, causing nontrivial holonomy in the Hilbert space bundle, which challenges the assumption of trivial geometry and highlights the bundle's topological complexity.

Contribution

It demonstrates that the full Hilbert space bundle can have nontrivial topology due to exceptional points, extending the understanding beyond eigenstate subbundles.

Findings

Exceptional points act as topological defects.

Nontrivial holonomy can occur in the full Hilbert space bundle.

The topology of the bundle is nontrivial due to these defects.

Abstract

Studies have shown that quantum states reside in a Hilbert space bundle. When a quantum system depends on continuous external parameters, these parameters define additional dimensions in the base space of the bundle. While much of the existing literature focuses on eigenstate subbundles, where geometric properties like Berry curvature arise, this work considers the entire Hilbert space bundle. Although the Hilbert space bundle has been found to be locally flat, suggesting that the system's geometry may appear trivial, we revisit this assumption. Specifically, we examine how an arbitrary quantum state evolves when transported along closed parameter loops, a phenomenon characterized by holonomy. Our results demonstrate that nontrivial holonomy can emerge in the presence of exceptional points. Consequently, the topology of the full Hilbert space bundle is nontrivial, with exceptional points acting as topological defects.