Real Non-Hermitian Energy Spectra Without Any Symmetry

TL;DR

This paper demonstrates that non-Hermitian systems can have real energy spectra and stability without relying on traditional symmetries, using the non-Hermitian skin effect as an alternative mechanism.

Contribution

It introduces minimal local models that achieve real spectra without symmetry constraints, expanding the understanding of non-Hermitian physics.

Findings

Models exhibit large parameter regions with real spectra without symmetry.

Non-reciprocal electrical circuits can implement these models.

The non-Hermitian skin effect can enforce real eigenenergies.

Abstract

Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic non-Hermitian phenomena. In this work, we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability. We showcase, for different classes of energy dispersions, various ansatz models that possess large parameter space regions with real spectra, despite not having any obvious symmetry. These minimal local models can be quickly implemented in non-reciprocal experimental setups such as electrical circuits with operational amplifiers.