Eigenstate clustering around exceptional points

Abstract

We propose an idea of eigenstate clustering in non-Hermitian systems. We show that nonorthogonal eigenstates can be clustered around exceptional points and illustrate our idea on some models. We discuss that exponential localization of eigenstates at edges due to the non-Hermitian skin effect is a typical example of eigenstate clustering. We numerically see that clustering of localized or extended eigenstates is possible in systems with both open and closed boundaries. We show that gain and loss can enhance eigenstate clustering. We use fidelities and the standard k-means clustering algorithm fora systematic study of clustered eigenstates.