Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge

Recently, an interesting family of quasiperiodic models with exact mobility edges（MEs） has been proposed（Phys.Rev. Lett. 114 146601（2015））. It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended（localized） states in the real space to l...

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Bibliographic Details
Published inChinese physics B Vol. 26; no. 7; pp. 323 - 327
Main Author 巩龙延 赵小新
Format Journal Article
LanguageEnglish
Published 01.06.2017
Subjects
Shannon信息熵
一维
周期模型
定位性能
对偶变换
相图
紧束缚模型
迁移率边
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Summary:Recently, an interesting family of quasiperiodic models with exact mobility edges（MEs） has been proposed（Phys.Rev. Lett. 114 146601（2015））. It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended（localized） states in the real space to localized（extended） ones in the Fourier space. Therefore,it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively.Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.
Bibliography:Long-Yan Gong1,2,3,Xiao-Xin Zhao2（ 1 Department of Applied Physics, Nanjing University of Posts and Telecommunications, Nanjing 210003, China; 2Institute of Signal Processing and Transmission, Nanjing University of Posts and Telecommunications, Nanjing 210003, China ; 3National Laboratory of Solid State Microstructures, Nanjing University, Nanjing 210093, China）
Anderson localization; quasiperiodic model; mobility edge
11-5639/O4
Recently, an interesting family of quasiperiodic models with exact mobility edges（MEs） has been proposed（Phys.Rev. Lett. 114 146601（2015））. It is self-dual under a generalized duality transformation. However, such transformation is not obvious to map extended（localized） states in the real space to localized（extended） ones in the Fourier space. Therefore,it needs more convictive evidences to confirm the existence of MEs. We use the second moment of wave functions, Shannon information entropies, and Lypanunov exponents to characterize the localization properties of the eigenstates, respectively.Furthermore, we obtain the phase diagram of the model. Our numerical results support the existing analytical findings.
ISSN:1674-1056
2058-3834
DOI:10.1088/1674-1056/26/7/077202