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 a...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.展开更多
This article reviews recent developments in the non-Hermitian skin effect(NHSE),particularly on its rich interplay with topology.The review starts off with a pedagogical introduction on the modified bulk-boundary corr...This article reviews recent developments in the non-Hermitian skin effect(NHSE),particularly on its rich interplay with topology.The review starts off with a pedagogical introduction on the modified bulk-boundary correspondence,the synergy and hybridization of NHSE and band topology in higher dimensions,as well as,the associated topology on the complex energy plane such as spectral winding topology and spectral graph topology.Following which,emerging topics are introduced such as non-Hermitian criticality,dynamical NHSE phenomena,and the manifestation of NHSE beyond the traditional linear non-interacting crystal lattices,particularly its interplay with quantum many-body interactions.Finally,we survey the recent demonstrations and experimental proposals of NHSE.展开更多
文摘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.
基金C.H.Lee acknowledges support from Singapore NRF’s QEP2.0 grant(NRF2021-QEP2-02-P09)MOE Tier-1 grant(WBS:A-8000022-00-00)+1 种基金L.Li acknowledges support from National Natural Science Foundation of China(Grant No.12104519)the Guangdong Project(Grant No.2021QN02X073).
文摘This article reviews recent developments in the non-Hermitian skin effect(NHSE),particularly on its rich interplay with topology.The review starts off with a pedagogical introduction on the modified bulk-boundary correspondence,the synergy and hybridization of NHSE and band topology in higher dimensions,as well as,the associated topology on the complex energy plane such as spectral winding topology and spectral graph topology.Following which,emerging topics are introduced such as non-Hermitian criticality,dynamical NHSE phenomena,and the manifestation of NHSE beyond the traditional linear non-interacting crystal lattices,particularly its interplay with quantum many-body interactions.Finally,we survey the recent demonstrations and experimental proposals of NHSE.
基金funding support by the National Natural Science Foundation of China (12104519)the Guangdong Basic and Applied Basic Research Foundation (2020A1515110773)
