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

doi:10.1088/1674-1056/ac11e5

中国物理B ›› 2021, Vol. 30 ›› Issue (9): 97202-097202.doi: 10.1088/1674-1056/ac11e5

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

Xiang-Ping Jiang(蒋相平)^1,2, Yi Qiao(乔艺)^1,†, and Jun-Peng Cao(曹俊鹏)^1,2,3,4

1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3 Songshan Lake Materials Laboratory, Dongguan 523808, China;
4 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China

收稿日期:2021-05-06 修回日期:2021-06-19 接受日期:2021-07-07 出版日期:2021-08-19 发布日期:2021-09-10
通讯作者: Yi Qiao E-mail:qiaoyi_joy@foxmail.com
基金资助:
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).

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

Xiang-Ping Jiang(蒋相平)^1,2, Yi Qiao(乔艺)^1,†, and Jun-Peng Cao(曹俊鹏)^1,2,3,4

1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, Beijing 100190, China;
2 School of Physical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China;
3 Songshan Lake Materials Laboratory, Dongguan 523808, China;
4 Peng Huanwu Center for Fundamental Theory, Xi'an 710127, China

Received:2021-05-06 Revised:2021-06-19 Accepted:2021-07-07 Online:2021-08-19 Published:2021-09-10
Contact: Yi Qiao E-mail:qiaoyi_joy@foxmail.com
Supported by:
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).

摘要/Abstract

摘要： 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.

关键词: Anderson localization, non-Hermitian quasiperiodic lattice, mobility edges

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.

Key words: Anderson localization, non-Hermitian quasiperiodic lattice, mobility edges

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)

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[J]. 中国物理B, 2021, 30(9): 97202-097202.

参考文献

[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

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

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

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