Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions

IF 11.6 1区 物理与天体物理 Q1 PHYSICS, MULTIDISCIPLINARY Physical Review X Pub Date : 2024-04-16 DOI:10.1103/physrevx.14.021011
Hong-Yi Wang, Fei Song, Zhong Wang
{"title":"Amoeba Formulation of Non-Bloch Band Theory in Arbitrary Dimensions","authors":"Hong-Yi Wang, Fei Song, Zhong Wang","doi":"10.1103/physrevx.14.021011","DOIUrl":null,"url":null,"abstract":"The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.","PeriodicalId":20161,"journal":{"name":"Physical Review X","volume":null,"pages":null},"PeriodicalIF":11.6000,"publicationDate":"2024-04-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Physical Review X","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1103/physrevx.14.021011","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MULTIDISCIPLINARY","Score":null,"Total":0}
引用次数: 0

Abstract

The non-Hermitian skin effect dramatically reshapes the energy bands of non-Hermitian systems, meaning that the usual Bloch band theory is fundamentally inadequate as their characterization. The non-Bloch band theory, in which the concept of Brillouin zone is generalized, has been widely applied to investigate non-Hermitian systems in one spatial dimension. However, its generalization to higher dimensions has been challenging. Here, we develop a formulation of the non-Hermitian skin effect and non-Bloch band theory in arbitrary spatial dimensions, which is based on a natural geometrical object known as the amoeba. Our theory provides a general framework for studying non-Hermitian bands beyond one dimension. Key quantities of non-Hermitian bands, including the energy spectrum, eigenstates profiles, and the generalized Brillouin zone, can be efficiently obtained from this approach.

Abstract Image

查看原文
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
任意维度非布洛克带理论的阿米巴公式
非ermitian趋肤效应极大地重塑了非ermitian系统的能带,这意味着通常的布洛赫能带理论根本不足以描述它们。非布洛赫能带理论是对布里渊区概念的概括,已被广泛应用于研究一维空间的非ermitian 系统。然而,将其推广到更高维度一直是个挑战。在这里,我们基于一个名为变形虫的自然几何物体,提出了任意空间维度的非ermitian趋肤效应和非布洛赫带理论。我们的理论为研究一维之外的非ermitian 带提供了一个通用框架。非赫米带的关键量,包括能谱、特征态剖面和广义布里渊区,都可以通过这种方法有效地获得。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 去求助
来源期刊
Physical Review X
Physical Review X PHYSICS, MULTIDISCIPLINARY-
CiteScore
24.60
自引率
1.60%
发文量
197
审稿时长
3 months
期刊介绍: Physical Review X (PRX) stands as an exclusively online, fully open-access journal, emphasizing innovation, quality, and enduring impact in the scientific content it disseminates. Devoted to showcasing a curated selection of papers from pure, applied, and interdisciplinary physics, PRX aims to feature work with the potential to shape current and future research while leaving a lasting and profound impact in their respective fields. Encompassing the entire spectrum of physics subject areas, PRX places a special focus on groundbreaking interdisciplinary research with broad-reaching influence.
期刊最新文献
Impact of Nuclear Motion on Light-Induced Bimolecular Interaction Dynamics Quantum Entanglement between Optical and Microwave Photonic Qubits Geometric Landscape Annealing as an Optimization Principle Underlying the Coherent Ising Machine Theory of Stimulated Brillouin Scattering in Fibers for Highly Multimode Excitations Theoretical Description of Pump-Probe Experiments in Charge-Density-Wave Materials out to Long Times
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1