Filling up complex spectral regions through non-Hermitian disordered chains

TL;DR

This paper introduces a method to construct non-Hermitian disordered chains with eigenspectra filling arbitrary regions in the complex plane, using specially designed random couplings that emulate semi-infinite boundary effects.

Contribution

The authors propose a novel, robust ansatz for creating models with prescribed spectral regions, utilizing non-Hermitian random couplings that are more local than traditional ensembles.

Findings

Eigenspectra can fill arbitrary regions in the complex plane.

The approach is feasible for implementation in physical systems.

The method exhibits high tolerance to imperfections.

Abstract

Eigenspectra that fill regions in the complex plane have been intriguing to many, inspiring research from random matrix theory to esoteric semi-infinite bounded non-Hermitian lattices. In this work, we propose a simple and robust ansatz for constructing models whose eigenspectra fill up generic prescribed regions. Our approach utilizes specially designed non-Hermitian random couplings that allow the co-existence of eigenstates with a continuum of localization lengths, mathematically emulating the effects of semi-infinite boundaries. While some of these couplings are necessarily long-ranged, they are still far more local than what is possible with known random matrix ensembles. Our ansatz can be feasibly implemented in physical platforms such as classical and quantum circuits, and harbors very high tolerance to imperfections due to its stochastic nature.