Invariable mobility edge in a quasiperiodic lattice

doi:10.1088/1674-1056/ac140e

中国物理B ›› 2022, Vol. 31 ›› Issue (2): 27101-027101.doi: 10.1088/1674-1056/ac140e

Invariable mobility edge in a quasiperiodic lattice

Tong Liu(刘通)^1,†, Shujie Cheng(成书杰)², Rui Zhang(张锐)¹, Rongrong Ruan(阮榕榕)¹, and Houxun Jiang(姜厚勋)¹

1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China

收稿日期:2021-05-22 修回日期:2021-06-23 接受日期:2021-07-14 出版日期:2022-01-13 发布日期:2022-01-13
通讯作者: Tong Liu E-mail:t6tong@njupt.edu.cn
基金资助:
T. Liu acknowledges X.-J. Liu for fruitful discussion. This work was supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200737), NUPTSF (Grants Nos. NY220090 and NY220208), and the National Natural Science Foundation of China (Grant No. 12074064), and the Innovation Research Project of Jiangsu Province, China (Grant No. JSSCBS20210521), and NJUPT-STITP (Grant No. XYB2021294).

Invariable mobility edge in a quasiperiodic lattice

Tong Liu(刘通)^1,†, Shujie Cheng(成书杰)², Rui Zhang(张锐)¹, Rongrong Ruan(阮榕榕)¹, and Houxun Jiang(姜厚勋)¹

1 School of Science, Nanjing University of Posts and Telecommunications, Nanjing 210003, China;
2 Department of Physics, Zhejiang Normal University, Jinhua 321004, China

Received:2021-05-22 Revised:2021-06-23 Accepted:2021-07-14 Online:2022-01-13 Published:2022-01-13
Contact: Tong Liu E-mail:t6tong@njupt.edu.cn
Supported by:
T. Liu acknowledges X.-J. Liu for fruitful discussion. This work was supported by the Natural Science Foundation of Jiangsu Province, China (Grant No. BK20200737), NUPTSF (Grants Nos. NY220090 and NY220208), and the National Natural Science Foundation of China (Grant No. 12074064), and the Innovation Research Project of Jiangsu Province, China (Grant No. JSSCBS20210521), and NJUPT-STITP (Grant No. XYB2021294).

摘要/Abstract

摘要： We analytically and numerically study a 1D tight-binding model with tunable incommensurate potentials. We utilize the self-dual relation to obtain the critical energy, namely, the mobility edge. Interestingly, we analytically demonstrate that this critical energy is a constant independent of strength of potentials. Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions, the inverse participation rate and the multifractal theory. All numerical results are in excellent agreement with the analytical results. 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.

关键词: Anderson localization, quasiperiodic, mobility edge, multifractal

Abstract: We analytically and numerically study a 1D tight-binding model with tunable incommensurate potentials. We utilize the self-dual relation to obtain the critical energy, namely, the mobility edge. Interestingly, we analytically demonstrate that this critical energy is a constant independent of strength of potentials. Then we numerically verify the analytical results by analyzing the spatial distributions of wave functions, the inverse participation rate and the multifractal theory. All numerical results are in excellent agreement with the analytical results. 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.

Key words: Anderson localization, quasiperiodic, mobility edge, multifractal

中图分类号: (Incommensurate crystals)

61.44.Fw

71.10.Fd (Lattice fermion models (Hubbard model, etc.)) 71.23.An (Theories and models; localized states)

Tong Liu(刘通), Shujie Cheng(成书杰), Rui Zhang(张锐), Rongrong Ruan(阮榕榕), and Houxun Jiang(姜厚勋). Invariable mobility edge in a quasiperiodic lattice[J]. 中国物理B, 2022, 31(2): 27101-027101.

Tong Liu(刘通), Shujie Cheng(成书杰), Rui Zhang(张锐), Rongrong Ruan(阮榕榕), and Houxun Jiang(姜厚勋). Invariable mobility edge in a quasiperiodic lattice[J]. Chin. Phys. B, 2022, 31(2): 27101-027101.

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Invariable mobility edge in a quasiperiodic lattice

Invariable mobility edge in a quasiperiodic lattice

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