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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 |
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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.
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Received: 08 January 2024
Revised: 27 February 2024
Accepted manuscript online: 15 March 2024
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Corresponding Authors:
Zhi-Jian Li
E-mail: zjli@sxu.edu.cn
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Cite this article:
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 2024 Chin. Phys. B 33 060301
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