Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

doi:10.1088/1674-1056/ac11e5

Abstract The mobility edges and reentrant localization transitions are studied in one-dimensional dimerized lattice with non-Hermitian either uniform or staggered quasiperiodic potentials. We find that the non-Hermitian uniform quasiperiodic disorder can induce an intermediate phase where the extended states coexist with the localized ones, which implies that the system has mobility edges. The localization transition is accompanied by the $\mathcal{PT}$ symmetry breaking transition. While if the non-Hermitian quasiperiodic disorder is staggered, we demonstrate the existence of multiple intermediate phases and multiple reentrant localization transitions based on the finite size scaling analysis. Interestingly, some already localized states will become extended states and can also be localized again for certain non-Hermitian parameters. The reentrant localization transitions are associated with the intermediate phases hosting mobility edges. Besides, we also find that the non-Hermiticity can break the reentrant localization transition where only one intermediate phase survives. More detailed information about the mobility edges and reentrant localization transitions are presented by analyzing the eigenenergy spectrum, inverse participation ratio, and normalized participation ratio.

Keywords: Anderson localization non-Hermitian quasiperiodic lattice mobility edges

Received: 06 May 2021
Revised: 19 June 2021
Accepted manuscript online: 07 July 2021

PACS:	61.44.Fw	(Incommensurate crystals)
	71.10.Fd	(Lattice fermion models (Hubbard model, etc.))
	71.23.An	(Theories and models; localized states)

Fund: Project supported by the National Key Research and Development Program of China (Grant Nos. 2016YFA0300600 and 2016YFA0302104), the National Natural Science Foundation of China (Grant Nos. 12074410, 12047502, 11934015, 11947301, and 11774397), the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB33000000), and the Fellowship of China Postdoctoral Science Foundation (Grant No. 2020M680724).

Corresponding Authors: Yi Qiao
E-mail: qiaoyi_joy@foxmail.com

Cite this article:

Xiang-Ping Jiang(蒋相平), Yi Qiao(乔艺), and Jun-Peng Cao(曹俊鹏) Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice 2021 Chin. Phys. B 30 097202

[1] Anderson P W 1958 Phys. Rev. 109 1492
[2] Abrahams E, Anderson P W, Licciardello D C and Ramakrishnan T V 1979 Phys. Rev. Lett. 42 673
[3] Lee P A and Ramakrishnan T V 1985 Rev. Mod. Phys. 57 287
[4] Evers F and Mirlin A D 2008 Rev. Mod. Phys. 80 1355
[5] Aubry S and André G 1980 Ann. Israel Phys. Soc 3 133
[6] Aubry S and André G 1980 Ann. Israel Phys. Soc 3 18
[7] Sarma SD, He S and Xie X C 1988 Phys. Rev. Lett. 61 2144
[8] Sarma S D, He S and Xie X C 1990 Phys. Rev. B 41 5544
[9] Biddle J and Sarma S D 2010 Phys. Rev. Lett. 104 070601
[10] Ganeshan S, Pixley J and Sarma S D 2015 Phys. Rev. Lett. 114 146601
[11] Luschen H P, Scherg S, Kohlert T, Schreiber M, Bordia P, Li X, Sarma S D and Bloch I 2018 Phys. Rev. Lett. 120 160404
[12] Wang Y, Xia X, Zhang L, Yao H, Chen S, You J, Zhou Q and Liu X 2020 Phys. Rev. Lett. 125 196604
[13] Roy S, Mishra T, Tanatar B and Basu S 2021 Phys. Rev. Lett. 126 106803
[14] Deng X L, Burin A L and Khaymovich I M 2020 arXiv:2002.00013
[15] Longhi S 2019 Phys. Rev. Lett. 122 237601
[16] Longhi S 2019 Phys. Rev. B 100 125157
[17] Jiang H, Lang L J, Yang C, Zhu S L and Chen S 2019 Phys. Rev. B 100 054301
[18] Zeng Q B, Yang Y B and Xu Y 2020 Phys. Rev. B 101 020201
[19] Cai X M 2021 Phys. Rev. B 103 014201
[20] Tang L Z, Zhang G Q, Zhang L F and Zhang D W 2021 Phys. Rev. A 103 033325
[21] Hou J, Wu Y J and Zhang C 2021 Phys. Rev. A 103 033305
[22] Huang Y and Shklovskii B I 2020 Phys. Rev. B 101 014204
[23] Tzortzakakis A F, Makris K G and Economou E N 2020 Phys. Rev. B 101 014202
[24] Luo X, Ohtsuki T and Shindou R 2021 Phys. Rev. Lett. 126 090402
[25] Luo X L, Ohtsuki T and Shindou R 2021 arXiv:2103.05239
[26] Kawabata K and Ryu S 2021 Phys. Rev. Lett. 126 166801
[27] Zhai L J, Huang G Y and Yin S 2021 Phys. Rev. B 104 014202
[28] Heiss W D 2012 J. Phys. A 45 444016
[29] Bender C and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[30] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[31] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801
[32] Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402
[33] Weidemann S, Kremer M, Longhi S and Szameit A 2020 arXiv:2007.00294
[34] Longhi S 2021 Phys. Rev. B 103 054203
[35] Tzortzakakis A F, Makris K G, Szameit A and Economou E N 2021 Phys. Rev. Research 3 013208
[36] Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570
[37] Hatano N and Nelson D R 1998 Phys. Rev. B 58 8384
[38] Zhou L W and Han W Q 2021 arXiv:2105.03302
[39] Liu Y, Jiang X P, Cao J and Chen S 2020 Phys. Rev. B 101 174205
[40] Zeng Q B and Xu Y 2020 Phys. Rev. Research 2 033052
[41] Liu T, Guo H, Pu Y and Longhi S 2020 Phys. Rev. B 102 024205
[42] Liu Y, Wang Y, Liu X J, Zhou Q and Chen S 2021 Phys. Rev. B 103 014203
[43] Liu Y X, Wang Y J, Zheng Z H and Chen S 2021 Phys. Rev. B 103 134208
[44] Su W P, Schrieffer J R and Heeger A J 1979 Phys. Rev. Lett. 42 1698
[45] Li X, Li X and Sarma S D 2017 Phys. Rev. B 96 085119
[46] Li X and Sarma S D 2020 Phys. Rev. B 101 064203

[1]	Anderson localization of a spin-orbit coupled Bose-Einstein condensate in disorder potential Huan Zhang(张欢), Sheng Liu(刘胜), and Yongsheng Zhang(张永生). Chin. Phys. B, 2022, 31(7): 070305.
[2]	Invariable mobility edge in a quasiperiodic lattice Tong Liu(刘通), Shujie Cheng(成书杰), Rui Zhang(张锐), Rongrong Ruan(阮榕榕), and Houxun Jiang(姜厚勋). Chin. Phys. B, 2022, 31(2): 027101.
[3]	Energy spreading, equipartition, and chaos in lattices with non-central forces Arnold Ngapasare, Georgios Theocharis, Olivier Richoux, Vassos Achilleos, and Charalampos Skokos. Chin. Phys. B, 2022, 31(2): 020506.
[4]	Energy relaxation in disordered lattice φ⁴ system: The combined effects of disorder and nonlinearity Jianjin Wang(汪剑津), Yong Zhang(张勇), and Daxing Xiong(熊大兴). Chin. Phys. B, 2020, 29(12): 120503.
[5]	Hidden Anderson localization in disorder-free Ising–Kondo lattice Wei-Wei Yang(杨薇薇), Lan Zhang(张欄), Xue-Ming Guo(郭雪明), and Yin Zhong(钟寅)†. Chin. Phys. B, 2020, 29(10): 107301.
[6]	Phase diagram of a family of one-dimensional nearest-neighbor tight-binding models with an exact mobility edge Long-Yan Gong(巩龙延), Xiao-Xin Zhao(赵小新). Chin. Phys. B, 2017, 26(7): 077202.
[7]	Uncertainties of clock and shift operators for an electron in one-dimensional nonuniform lattice systems Long-Yan Gong(巩龙延), You-Gen Ding(丁友根), Yong-Qiang Deng(邓永强). Chin. Phys. B, 2017, 26(11): 117201.
[8]	Disordered quantum walks in two-dimensional lattices Zhang Rong(张融), Xu Yun-Qiu(徐韵秋), Xue Peng(薛鹏). Chin. Phys. B, 2015, 24(1): 010303.
[9]	Transport dynamics of an interacting binary Bose–Einstein condensate in an incommensurate optical lattice Cui Guo-Dong (崔国栋), Sun Jian-Fang (孙剑芳), Jiang Bo-Nan (姜伯楠), Qian Jun (钱军), Wang Yu-Zhu (王育竹). Chin. Phys. B, 2013, 22(10): 100501.
[10]	State vector evolution localized over the edges of a square tight-binding lattice He Liang-Ming(何良明) and Shi Duan-Wen (石端文). Chin. Phys. B, 2009, 18(3): 1214-1220.

No Suggested Reading articles found!

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Mobility edges and reentrant localization in one-dimensional dimerized non-Hermitian quasiperiodic lattice

Cite this article:

Online attention