Invariable mobility edge in a quasiperiodic lattice

In this paper, we study a one-dimensional tight-binding model with tunable incommensurate potentials. Through the analysis of the inverse participation rate, we uncover that the wave functions corresponding to the energies of the system exhibit different properties. There exists a critical energy un...

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Bibliographic Details
Published in:arXiv.org 2021-05
Main Authors: Liu, Tong, Zhu, Yufei, Cheng, Shujie, Li, Feng, Guo, Hao, Pu, Yong
Format: Article
Language:English
Subjects:
Optical lattices
Spatial distribution
Wave functions
Online Access:Get full text
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Summary:In this paper, we study a one-dimensional tight-binding model with tunable incommensurate potentials. Through the analysis of the inverse participation rate, we uncover that the wave functions corresponding to the energies of the system exhibit different properties. There exists a critical energy under which the wave functions corresponding to all energies are extended. On the contrary, the wave functions corresponding to all energies above the critical energy are localized. However, we are surprised to find that the critical energy is a constant independent of the potentials. We use the self-dual relation to solve the critical energy, namely the mobility edge, and then we verify the analytical results again by analyzing the spatial distributions of the wave functions. Finally, we give a brief discussion on the possible experimental observation of the invariable mobility edge in the system of ultracold atoms in optical lattices.
ISSN:2331-8422
DOI:10.48550/arxiv.2101.00177