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Chin. Phys. B, 2024, Vol. 33(6): 060301    DOI: 10.1088/1674-1056/ad342d
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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
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.
Keywords:  quantum walk      mobility edges      quasiperiodicity  
Received:  08 January 2024      Revised:  27 February 2024      Accepted manuscript online:  15 March 2024
PACS:  03.65.-w (Quantum mechanics)  
  03.67. Lx  
  05.60.Gg (Quantum transport)  
Corresponding Authors:  Zhi-Jian Li     E-mail:  zjli@sxu.edu.cn

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

[1] Aharonov Y, Davidovich L and Zagury N 1993 Phys. Rev. A 48 1687
[2] Kempe J 2003 Contemp. Phys. 44 307
[3] Venegas-Andraca S E 2012 Quantum Inf. Process. 11 1015
[4] Childs A M 2009 Phys. Rev. Lett. 102 180501
[5] Kitagawa T, Berg E, Rudner M and Demler E 2010 Phys. Rev. B 82 235114
[6] Anderson P W 1958 Phys. Rev. 109 1492
[7] Mochizuki K, Kim D and Obuse H 2016 Phys. Rev. A 93 062116
[8] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[9] Zhou H and Lee J Y 2019 Phys. Rev. B 99 235112
[10] Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402
[11] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[12] Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570
[13] Hatano N and Nelson D R 1998 Phys. Rev. B 58 8384
[14] Kolesnikov A V and Efetov K B 2000 Phys. Rev. Lett. 84 5600
[15] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079
[16] Harper P G 1955 Proc. Phys. Soc. A 68 874
[17] Liu Y, Wang Y, Liu X J, Zhou Q and Chen S 2021 Phys. Rev. B 103 014203
[18] Liu Y, Wang Y, Zheng Z and Chen S 2021 Phys. Rev. B 103 134208
[19] Longhi S 2021 Phys. Rev. B 103 054203
[20] Acharya A P, Chakrabarty A, Sahu D K and Datta S 2022 Phys. Rev. B 105 014202
[21] Lin Q, Li T, Xiao L, Wang K, Yi W and Xue P 2022 Nat. Commun. 13 3229
[22] Xiao L, Deng T, Wang K, Wang Z, Yi W and Xue P 2021 Phys. Rev. Lett. 126 230402
[23] Wang Y, Xia X, Zhang L, Yao H, Chen S, You J, Zhou Q and Liu X J 2020 Phys. Rev. Lett. 125 196604
[24] Wang Y, Zhang L, Wan Y, He Y and Wang Y 2023 Phys. Rev. B 107 L140201
[25] Jiang H, Lang L J, Yang C, Zhu S L and Chen S 2019 Phys. Rev. B 100 054301
[26] Xiong Y 2018 J. Phys. Commun. 2 035043
[27] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401
[28] Guo C X, Liu C H, Zhao X M, Liu Y and Chen S 2021 Phys. Rev. Lett. 127 116801
[29] Liu Y, Zeng Y, Li L and Chen S 2021 Phys. Rev. B 104 085401
[30] Li Z J, Izaac J A and Wang J B 2013 Phys. Rev. A 87 012314
[31] Schreiber M 1985 J. Phys. C: Solid State Phys. 18 2493
[32] Wegner F 1980 Z. Physik B 36 209
[33] Lin X, Chen X, Guo G C and Gong M 2023 Phys. Rev. B 108 174206
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