Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings

Li Wang, Jiaqi Liu, Zhenbo Wang, Shu Chen
{"title":"Exact complex mobility edges and flagellate spectra for non-Hermitian quasicrystals with exponential hoppings","authors":"Li Wang, Jiaqi Liu, Zhenbo Wang, Shu Chen","doi":"arxiv-2406.10769","DOIUrl":null,"url":null,"abstract":"We propose a class of general non-Hermitian quasiperiodic lattice models with\nexponential hoppings and analytically determine the genuine complex mobility\nedges by solving its dual counterpart exactly utilizing Avila's global theory.\nOur analytical formula unveils that the complex mobility edges usually form a\nloop structure in the complex energy plane. By shifting the eigenenergy a\nconstant $t$, the complex mobility edges of the family of models with different\nhopping parameter $t$ can be described by a unified formula, formally\nindependent of $t$. By scanning the hopping parameter, we demonstrate the\nexistence of a type of intriguing flagellate-like spectra in complex energy\nplane, in which the localized states and extended states are well separated by\nthe complex mobility edges. Our result provides a firm ground for understanding\nthe complex mobility edges in non-Hermitian quasiperiodic lattices.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-06-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2406.10769","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0

Abstract

We propose a class of general non-Hermitian quasiperiodic lattice models with exponential hoppings and analytically determine the genuine complex mobility edges by solving its dual counterpart exactly utilizing Avila's global theory. Our analytical formula unveils that the complex mobility edges usually form a loop structure in the complex energy plane. By shifting the eigenenergy a constant $t$, the complex mobility edges of the family of models with different hopping parameter $t$ can be described by a unified formula, formally independent of $t$. By scanning the hopping parameter, we demonstrate the existence of a type of intriguing flagellate-like spectra in complex energy plane, in which the localized states and extended states are well separated by the complex mobility edges. Our result provides a firm ground for understanding the complex mobility edges in non-Hermitian quasiperiodic lattices.
具有指数跳跃的非赫米提准晶体的精确复迁移率边缘和鞭毛虫光谱
我们提出了一类具有指数跳跃的一般非ermitian准周期晶格模型,并通过利用阿维拉全局理论精确求解其对偶对应物,分析确定了真正的复流动边。我们的分析公式揭示了复流动边通常在复能面上形成环状结构。通过移动特征能常数 $t$,具有不同跳变参数 $t$ 的模型族的复流动边可以用一个统一的公式来描述,形式上与 $t$ 无关。通过扫描跳变参数,我们证明了在复能面上存在一种有趣的类似鞭毛虫的光谱,在这种光谱中,局部态和扩展态被复迁移率边沿很好地分开。我们的结果为理解非ermitian 准周期晶格中的复流动边缘提供了坚实的基础。
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 求助全文
来源期刊
自引率
0.00%
发文量
0
×
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
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信