General theory for infernal points in non-Hermitian systems

TL;DR

This paper develops a comprehensive theoretical framework for understanding infernal points, where many eigenstates coalesce in non-Hermitian systems, explaining their localization and coalescence mechanisms across various dimensions.

Contribution

It introduces a general theory for infernal points in open-boundary non-Hermitian systems using non-Bloch band theory and amoeba formulation, applicable to arbitrary dimensions.

Findings

Criteria for the presence of infernal points established

Explanation of wave function localization at infernal points

Mechanism for eigenstate coalescence unveiled

Abstract

The coalescence of eigenstates is a unique phenomena in non-Hermitian systems. Remarkably, it has been noticed in some non-Hermitian systems under open boundary conditions that the whole set of eigenstates can coalesce to only a few eigenstates. In the parameter space, the point at which such a coalescence of macroscopic eigenstates occurs is dubbed as an infernal point. In this paper, based on the non-Bloch band theory and amoeba formulation, we establish the criteria for the presence of infernal points in one-dimensional and higher dimensional open-boundary non-Hermitian systems. In addition, we find an explanation of the extreme localization of the wave functions and unveil the mechanism for the coalescence of enormous eigenstates at the infernal points. Our work provides a general theory for infernal points in open-boundary non-Hermitian systems in arbitrary dimensions, and hence paves the way to study the intriguing infernal points systematically.