Filling up complex spectral regions through non-Hermitian disordered chains

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.

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Cited by in corpus (9)

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• Dimensional transmutation from non-Hermiticity
• Universal competitive spectral scaling from the critical non-Hermitian skin effect
• Designing non-Hermitian real spectra through electrostatics
• Nonequilibrium dynamics of the localization-delocalization transition in the non-Hermitian Aubry-André model
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• Phase transitions in non-Hermitian superlattices
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