Eigenstate clustering around exceptional points

TL;DR

This paper introduces the concept of eigenstate clustering in non-Hermitian systems, demonstrating how eigenstates can cluster around exceptional points and be influenced by gain, loss, and boundary conditions.

Contribution

It presents a novel idea of eigenstate clustering around exceptional points and explores how non-Hermitian effects like the skin effect and gain/loss influence this phenomenon.

Findings

Eigenstates can cluster around exceptional points in non-Hermitian systems.

Eigenstate clustering occurs in both open and closed boundary systems.

Gain and loss can enhance the clustering of eigenstates.

Abstract

We propose an idea of eigenstate clustering in non-Hermitian systems. We show that non-orthogonal 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 are 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 for a systematic study of clustered eigenstates.