Filling up complex spectral regions through non-Hermitian disordered chains

doi:10.1088/1674-1056/ac4a73

摘要/Abstract

摘要： 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.

关键词: non-Hermitian skin effect, disordered chain, disorder localization, non-Hermitian spectra

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.

Key words: non-Hermitian skin effect, disordered chain, disorder localization, non-Hermitian spectra

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

05.50.+q (Lattice theory and statistics) 64.70.Tg (Quantum phase transitions) 71.55.Jv (Disordered structures; amorphous and glassy solids)

Hui Jiang and Ching Hua Lee. Filling up complex spectral regions through non-Hermitian disordered chains[J]. 中国物理B, 2022, 31(5): 50307-050307.

Hui Jiang and Ching Hua Lee. Filling up complex spectral regions through non-Hermitian disordered chains[J]. Chin. Phys. B, 2022, 31(5): 50307-050307.

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