General Exceptional Points

TL;DR

This paper introduces the concept of general exceptional points (GEPs) in non-Hermitian physics, emphasizing basis defectiveness over traditional degeneracy, and explores their properties and classifications through topological models.

Contribution

It proposes the universal feature of basis defectiveness as a key aspect of GEPs, expanding the understanding of non-Hermitian degeneracies beyond energy degeneracy.

Findings

GEPs are characterized by basis defectiveness rather than energy degeneracy.

Different types of GEPs exhibit unique topological and phase transition properties.

Edge states in the non-Hermitian SSH model illustrate the physical nature of GEPs.

Abstract

Exceptional points are interesting physical phenomena in non-Hermitian physics at which the eigenvalues are degenerate and the eigenvectors coalesce. In this paper, we find that the universal feature of arbitrary non-Hermitian two level systems with singularities is basis defectiveness rather than energy degeneracy or state coalescence. This leads to the discovery of general exceptional points (GEPs). For GEPs, more subtle structures (e.g., Bloch peach), additional classification, and' 'hidden" quantum phase transitions are explored. By using the topologically protected subspace from two edge states in the non-Hermitian SSH model as an example, we illustrate the physical properties of different types of GEPs.