Almost mobility edges and the existence of critical regions in one-dimensional quasiperiodic lattices

2016/07/18 by Yucheng Wang, Gao Xianlong, Shu Chen
Materials Science · Physics and Astronomy · #Delocalized electron #Eigenvalues and eigenvectors #Limit (mathematics) #Multifractal system #Nonlinear Photonic Systems #Quasicrystal Structures and Properties #Quasiperiodic function #Quasiperiodicity #Topological Materials and Phenomena #Wave vector #Work (physics) #cond-mat.dis-nn

paper · pdf · doi:10.1140/epjb/e2017-80232-3

published as Eur. Phys. J. B 90, 215 (2017) · 8 pages, 11 figures

arxiv created 2016/07/18 · openalex created_date 2016/08/23 · openalex publication_date 2017/11/01 · arxiv updated 2018/01/03 · openalex updated_date 2026/08/05

Abstract

We study a one-dimensional quasiperiodic system described by the Aubry-André model in the small wave vector limit and demonstrate the existence of almost mobility edges and critical regions in the system. It is well known that the eigenstates of the Aubry-André model are either extended or localized depending on the strength of incommensurate potential V being less or bigger than a critical value V_c, and thus no mobility edge exists. However, it was shown in a recent work that this conclusion does not hold true when the wave vector α of the incommensurate potential is small, and for the system with V<V_c, there exist almost mobility edges at the energy E_c_±, which separate the robustly delocalized states from "almost localized" states. We find that, besides E_c_±, there exist additionally another energy edges E_c'_±, at which abrupt change of inverse participation ratio occurs. By using the inverse participation ratio and carrying out multifractal analyses, we identify the existence of critical regions among |E_c_±| ≤ |E| ≤ |E_c'_±| with the almost mobility edges E_c_± and E_c'_± separating the critical region from the extended and localized regions, respectively. We also study the system with V>V_c, for which all eigenstates are localized states, but can be divided into extended, critical and localized states in their dual space by utilizing the self-duality property of the Aubry-André model.

Citations

• Topological Superconductor to Anderson Localization Transition in One-Dimensional Incommensurate Lattices
• Localization by bichromatic potentials versus Anderson localization
• Two Scenarios for Quantum Multifractality Breakdown
• Delocalization and Heisenberg's uncertainty relation
• Noise correlation scalings: Revisiting the quantum phase transition in incommensurate lattices with hard-core bosons
• Electrons in disordered systems and the theory of localization
• Quasiperiodic Bose-Hubbard model and localization in one-dimensional cold atomic gases