Eigenstate clustering around exceptional points

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.

To Appear in Physical Review A

References in corpus (5)

• Topological Origin of Non-Hermitian Skin Effects
• New topological invariants in non-Hermitian systems
• Topological phase in a non-Hermitian PT symmetric system
• Topological states in non-Hermitian two-dimensional Su-Schrieffer-Heeger model
• Non-Hermitian phase transition and eigenstate localization induced by asymmetric coupling