{"title":"一维非赫米提准晶体中的精确反常迁移率边缘","authors":"Xiang-Ping Jiang, Weilei Zeng, Yayun Hu, Lei Pan","doi":"arxiv-2409.03591","DOIUrl":null,"url":null,"abstract":"Recent research has made significant progress in understanding localization\ntransitions and mobility edges (MEs) that separate extended and localized\nstates in non-Hermitian (NH) quasicrystals. Here we focus on studying critical\nstates and anomalous MEs, which identify the boundaries between critical and\nlocalized states within two distinct NH quasiperiodic models. Specifically, the\nfirst model is a quasiperiodic mosaic lattice with both nonreciprocal hopping\nterm and on-site potential. In contrast, the second model features an unbounded\nquasiperiodic on-site potential and nonreciprocal hopping. Using Avila's global\ntheory, we analytically derive the Lyapunov exponent and exact anomalous MEs.\nTo confirm the emergence of the robust critical states in both models, we\nconduct a numerical multifractal analysis of the wave functions and spectrum\nanalysis of level spacing. Furthermore, we investigate the transition between\nreal and complex spectra and the topological origins of the anomalous MEs. Our\nresults may shed light on exploring the critical states and anomalous MEs in NH\nquasiperiodic systems.","PeriodicalId":501066,"journal":{"name":"arXiv - PHYS - Disordered Systems and Neural Networks","volume":"57 1","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Exact anomalous mobility edges in one-dimensional non-Hermitian quasicrystals\",\"authors\":\"Xiang-Ping Jiang, Weilei Zeng, Yayun Hu, Lei Pan\",\"doi\":\"arxiv-2409.03591\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Recent research has made significant progress in understanding localization\\ntransitions and mobility edges (MEs) that separate extended and localized\\nstates in non-Hermitian (NH) quasicrystals. Here we focus on studying critical\\nstates and anomalous MEs, which identify the boundaries between critical and\\nlocalized states within two distinct NH quasiperiodic models. Specifically, the\\nfirst model is a quasiperiodic mosaic lattice with both nonreciprocal hopping\\nterm and on-site potential. In contrast, the second model features an unbounded\\nquasiperiodic on-site potential and nonreciprocal hopping. Using Avila's global\\ntheory, we analytically derive the Lyapunov exponent and exact anomalous MEs.\\nTo confirm the emergence of the robust critical states in both models, we\\nconduct a numerical multifractal analysis of the wave functions and spectrum\\nanalysis of level spacing. Furthermore, we investigate the transition between\\nreal and complex spectra and the topological origins of the anomalous MEs. Our\\nresults may shed light on exploring the critical states and anomalous MEs in NH\\nquasiperiodic systems.\",\"PeriodicalId\":501066,\"journal\":{\"name\":\"arXiv - PHYS - Disordered Systems and Neural Networks\",\"volume\":\"57 1\",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-05\",\"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-2409.03591\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - PHYS - Disordered Systems and Neural Networks","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.03591","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
最近的研究在理解非ermitian(NH)准晶体中分离扩展态和局部态的局部化转变和迁移率边缘(MEs)方面取得了重大进展。在这里,我们重点研究临界状态和反常移动边(ME),它们确定了两个不同的 NH 准周期模型中临界状态和局部状态之间的边界。具体来说,第一个模型是一个具有非互惠跳动项和现场势的准周期镶嵌晶格。与此相反,第二种模型具有无约束的准周期现场电势和非互惠跳变。为了证实这两个模型都出现了稳健临界态,我们对波函数进行了数值多分形分析,并对级距进行了谱分析。此外,我们还研究了真实光谱和复数光谱之间的过渡以及异常 ME 的拓扑起源。我们的研究结果可能有助于探索 NH 夸周期系统中的临界状态和反常 ME。
Exact anomalous mobility edges in one-dimensional non-Hermitian quasicrystals
Recent research has made significant progress in understanding localization
transitions and mobility edges (MEs) that separate extended and localized
states in non-Hermitian (NH) quasicrystals. Here we focus on studying critical
states and anomalous MEs, which identify the boundaries between critical and
localized states within two distinct NH quasiperiodic models. Specifically, the
first model is a quasiperiodic mosaic lattice with both nonreciprocal hopping
term and on-site potential. In contrast, the second model features an unbounded
quasiperiodic on-site potential and nonreciprocal hopping. Using Avila's global
theory, we analytically derive the Lyapunov exponent and exact anomalous MEs.
To confirm the emergence of the robust critical states in both models, we
conduct a numerical multifractal analysis of the wave functions and spectrum
analysis of level spacing. Furthermore, we investigate the transition between
real and complex spectra and the topological origins of the anomalous MEs. Our
results may shed light on exploring the critical states and anomalous MEs in NH
quasiperiodic systems.