Exceptional classifications of non-Hermitian systems

Abstract

Eigenstate coalescence in non-Hermitian systems is widely observed in diverse scientific domains encompassing optics and open quantum systems. Recent investigations have revealed that adiabatic encircling of exceptional points (EPs) leads to a nontrivial Berry phase in addition to an exchange of eigenstates. Based on these phenomena, we propose in this work an exhaustive classification framework for EPs in non Hermitian physical systems. In contrast to previous classifications that only incorporate the eigenstate exchange effect, our proposed classification gives rise to finer Z2 classifications depending on the presence of a π Berry phase after the encircling of the EPs. Moreover, by mapping arbitrary one-dimensional systems to the adiabatic encircling of EPs, we can classify onedimensional non-Hermitian systems characterized by topological phase transitions involving EPs. Applying our exceptional classification to various multiband systems, we expect to enhance the understanding of topological phases in non-Hermitian systems.