Classical correspondence of the exceptional points in the finite non-Hermitian system

TL;DR

This paper explores the topological structure of exceptional points in finite non-Hermitian systems, revealing their vortex-like nature and classical correspondence through Berry connection and curvature, exemplified by the non-Hermitian Rice-Mele model.

Contribution

It demonstrates the classical correspondence of exceptional lines in finite non-Hermitian systems using Berry connection and curvature, with application to the Rice-Mele model.

Findings

Exceptional lines act as vortex filaments with identifiable directions.

Boundary exceptional lines are topological, non-boundary are not.

Berry phase depends on the path around boundary exceptional lines.

Abstract

We systematically study the topology of the exceptional point (EP) in the finite non-Hermitian system. Based on the concrete form of the Berry connection, we demonstrate that the exceptional line (EL), at which the eigenstates coalesce, can act as a vortex filament. The direction of the EL can be identified by the corresponding Berry curvature. In this context, such a correspondence makes the topology of the EL clear at a glance. As an example, we apply this finding to the non-Hermitian Rice-Mele (RM) model, the non-Hermiticity of which arises from the staggered on-site complex potential. The boundary ELs are topological, but the non-boundary ELs are not. Each non-boundary EL corresponds to two critical momenta that make opposite contributions to the Berry connection. Therefore, the Berry connection of the many-particle quantum state can have classical correspondence, which is determined merely by the boundary ELs. Furthermore, the non-zero Berry phase, which experiences a closed path in the parameter space, is dependent on how the curve surrounds the boundary EL. This also provides an alternative way to investigate the topology of the EP and its physical correspondence in a finite non-Hermitian system.