Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

doi:10.1088/1674-1056/ad342d

中国物理B ›› 2024, Vol. 33 ›› Issue (6): 60301-060301.doi: 10.1088/1674-1056/ad342d

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

Xin-Hui Cui(崔鑫辉), Hui-Min Wang(王慧敏), and Zhi-Jian Li(李志坚)†

Institute of Theoretical Physics, State Key Laboratory of Quantum Optics and Quantum Devices, Shanxi University, Taiyuan 030006, China

收稿日期:2024-01-08 修回日期:2024-02-27 接受日期:2024-03-15 出版日期:2024-06-18 发布日期:2024-06-18
通讯作者: Zhi-Jian Li E-mail:zjli@sxu.edu.cn

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

Xin-Hui Cui(崔鑫辉), Hui-Min Wang(王慧敏), and Zhi-Jian Li(李志坚)†

Institute of Theoretical Physics, State Key Laboratory of Quantum Optics and Quantum Devices, Shanxi University, Taiyuan 030006, China

Received:2024-01-08 Revised:2024-02-27 Accepted:2024-03-15 Online:2024-06-18 Published:2024-06-18
Contact: Zhi-Jian Li E-mail:zjli@sxu.edu.cn

摘要/Abstract

摘要： We construct a one-dimensional quasiperiodic quantum walk to investigate the localization-delocalization transition. The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

关键词: quantum walk, mobility edges, quasiperiodicity

Abstract: We construct a one-dimensional quasiperiodic quantum walk to investigate the localization-delocalization transition. The inverse participation ratio and Lyapunov exponent are employed as two indexes to determine the mobility edge, a critical energy to distinguish the energy regions of extended and localized states. The analytical solution of mobility edge is obtained by the Lyapunov exponents in global theory, and the consistency of the two indexes is confirmed. We further study the dynamic characteristics of the quantum walk and show that the probabilities are localized to some specific lattice sites with time evolution. This phenomenon is explained by the effective potential of the Hamiltonian which corresponds to the phase in the coin operator of the quantum walk.

Key words: quantum walk, mobility edges, quasiperiodicity

中图分类号: (Quantum mechanics)

03.65.-w

05.60.Gg (Quantum transport)

Xin-Hui Cui(崔鑫辉), Hui-Min Wang(王慧敏), and Zhi-Jian Li(李志坚). Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk[J]. 中国物理B, 2024, 33(6): 60301-060301.

Xin-Hui Cui(崔鑫辉), Hui-Min Wang(王慧敏), and Zhi-Jian Li(李志坚). Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk[J]. Chin. Phys. B, 2024, 33(6): 60301-060301.

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Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

Mobility edges and localization characteristics in one-dimensional quasiperiodic quantum walk

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