Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

doi:10.1088/1674-1056/ac3228

中国物理B ›› 2022, Vol. 31 ›› Issue (1): 10313-010313.doi: 10.1088/1674-1056/ac3228

所属专题： SPECIAL TOPIC — Non-Hermitian physics

Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

Cui-Xian Guo(郭翠仙)¹ and Shu Chen(陈澍)^1,2,3,†

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 Yangtze River Delta Physics Research Center, Liyang 213300, China

收稿日期:2021-09-13 修回日期:2021-10-19 接受日期:2021-10-22 出版日期:2021-12-03 发布日期:2021-12-23
通讯作者: Shu Chen E-mail:schen@iphy.ac.cn
基金资助:
Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0300600), the National Natural Science Foundation of China (Grant No. 11974413), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB33000000).

Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

Cui-Xian Guo(郭翠仙)¹ and Shu Chen(陈澍)^1,2,3,†

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 Yangtze River Delta Physics Research Center, Liyang 213300, China

Received:2021-09-13 Revised:2021-10-19 Accepted:2021-10-22 Online:2021-12-03 Published:2021-12-23
Contact: Shu Chen E-mail:schen@iphy.ac.cn
Supported by:
Project supported by the National Key Research and Development Program of China (Grant No. 2016YFA0300600), the National Natural Science Foundation of China (Grant No. 11974413), and the Strategic Priority Research Program of Chinese Academy of Sciences (Grant No. XDB33000000).

摘要/Abstract

摘要： We study the one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore how to analytically solve the systems under some specific boundary conditions. Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters, we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations, which give the specific boundary conditions. Our analytical results show that the wave functions take simple forms and are independent of hopping range, while the eigenvalue spectra display rich model-dependent structures. Particularly, we find the existence of a special point coined as pseudo-periodic boundary condition, for which the eigenvalues are the same as those of the periodical system when the hopping parameters fulfill certain conditions, whereas the eigenstates display the non-Hermitian skin effect.

关键词: non-Hermitian physics, exact solution, topological physics, long-range hopping

Abstract: We study the one-dimensional general non-Hermitian models with asymmetric long-range hopping and explore how to analytically solve the systems under some specific boundary conditions. Although the introduction of long-range hopping terms prevents us from finding analytical solutions for arbitrary boundary parameters, we identify the existence of exact solutions when the boundary parameters fulfill some constraint relations, which give the specific boundary conditions. Our analytical results show that the wave functions take simple forms and are independent of hopping range, while the eigenvalue spectra display rich model-dependent structures. Particularly, we find the existence of a special point coined as pseudo-periodic boundary condition, for which the eigenvalues are the same as those of the periodical system when the hopping parameters fulfill certain conditions, whereas the eigenstates display the non-Hermitian skin effect.

Key words: non-Hermitian physics, exact solution, topological physics, long-range hopping

中图分类号: (Decoherence; open systems; quantum statistical methods)

03.65.Yz

03.65.Fd (Algebraic methods) 03.65.Vf (Phases: geometric; dynamic or topological)

Cui-Xian Guo(郭翠仙) and Shu Chen(陈澍). Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions[J]. 中国物理B, 2022, 31(1): 10313-010313.

Cui-Xian Guo(郭翠仙) and Shu Chen(陈澍). Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions[J]. Chin. Phys. B, 2022, 31(1): 10313-010313.

参考文献

[1] Ashida Y, Gong Z and Ueda M 2020 Adv. Phys. 69 249
[2] Bergholtz E J, Budich J C and Kunst F K Rev. Mod. Phys. 93 015005
[3] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079
[4] Kawabata K, Shiozaki K, Ueda M and Sato M 2019 Phys. Rev. X 9 041015
[5] Zhou H and Lee J Y 2019 Phys. Rev. B 99 235112
[6] Liu C H, Jiang H and Chen S 2019 Phys. Rev. B 99 125103
[7] Liu C H and Chen S 2019 Phys. Rev. B 100 144106
[8] Lee T E 2016 Phys. Rev. Lett. 116 133903
[9] Yin C, Jiang H, Li L, Lü R and Chen S 2018 Phys. Rev. A 97 052115
[10] Jiang H, Yang C and Chen S 2018 Phys. Rev. A 98 052116
[11] Xiong Y 2018 J. Phys. Commun. 2 035043
[12] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401(R)
[13] Leykam D, Bliokh K Y, Huang C, Chong Y D and Nori F 2017 Phys. Rev. Lett. 118 040401
[14] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[15] Shen H, Zhen B and Fu L 2018 Phys. Rev. Lett. 120, 146402
[16] Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808
[17] Yao S, Song F and Wang Z 2018 Phys. Rev. Lett. 121 136802
[18] Lee C H and Thomale R 2019 Phys. Rev. B 99 201103
[19] Yokomizo K and Murakami S 2019 Phys. Rev. Lett. 123 066404
[20] Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402
[21] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801
[22] Jiang H, Lang L J, Yang C, Zhu S L and Chen S 2019 Phys. Rev. B 100, 054301
[23] Jin L and Song Z 2019 Phys. Rev. B 99 081103(R)
[24] Borgnia D S, Kruchkov A J and Slager R J 2020 Phys. Rev. Lett. 124 056802
[25] Longhi S 2019 Phys. Rev. Research 1 023013
[26] Herviou L, Bardarson J H and Regnault N 2019 Phys. Rev. A 99 052118
[27] Imura K I and Takane Y 2019 Phys. Rev. B 100 165430
[28] Lee C H, Li L and Gong J 2019 Phys. Rev. Lett. 123 016805
[29] Deng T S and Yi W 2019 Phys. Rev. B 100 035102
[30] Ezawa M 2019 Phys. Rev. B 99 121411(R)
[31] Wang X R, Guo C X and Kou S P 2020 Phys. Rev. B 101 121116
[32] Yang Z, Zhang K, Fang C and Hu J 2020 Phys. Rev. Lett. 125 226402
[33] Lee C H, Li L, Thomale R and Gong J 2020 Phys. Rev. B 102 085151
[34] Ozcakmakli Turker Z and Yuce C 2019 Phys. Rev. A 99 022127
[35] Liu Y X and Chen S 2020 Phys. Rev. B 102 075404
[36] Lang L J, Wang Y, Wang H and Chong Y D 2018 Phys. Rev. B 98 094307
[37] Jiang H, Lü R and Chen S 2020 Eur. Phys. J. B 93 125
[38] Guo C X, Liu C H, Zhao X M, Liu Y and Chen S 2021 Phys. Rev. Lett. 127 116801
[39] Liu Y, Zeng Y, Li L and Chen S 2021 Phys. Rev. B 104 085401
[40] Roccati F 2021 Phys. Rev. A 104 022215
[41] Koch R and Budich J C 2020 Eur. Phys. J. D 74 70
[42] Li L, Lee C H and Gong J 2021 Commun. Phys. 4 42
[43] Li L, Lee C H, Mu S and Gong J 2020 Nat. Commun. 11 5491
[44] Liu C H, Zhang K, Yang Z and Chen S 2020 Phys. Rev. Research 2 043167
[45] Hatano N and Nelson D R 1996 Phys. Rev. Lett. 77 570
[46] Hatano N and Nelson D R 1997 Phys. Rev. B 56 8651
[47] Hatano N and Nelson D R 1997 Phys. Rev. B 56 8651
[48] Helbig T, Hofmann T, Imhof S, Abdelghany M, Kiessling T, Molenkamp L W, Lee C H, Szameit A, Greiter M and Thomale R 2020 Nat. Phys. 16 747
[49] Liu S, Shao R, Ma S, Zhang L, You O, Wu H, Xiang Y J, Cui T J and Zhang S 2021 Research 2021 5608038

Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

Exact solutions of non-Hermitian chains with asymmetric long-range hopping under specific boundary conditions

RichHTML

PDF (PC)

赞

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

Metrics

本文评价

推荐阅读 0

[1]	Boxue Zhang(张博学), Qingya Li(李青铔), Xiao Zhang(张笑), and Ching Hua Lee(李庆华). Real non-Hermitian energy spectra without any symmetry[J]. 中国物理B, 2022, 31(7): 70308-070308.
[2]	Anwei Zhang(张安伟). Revealing Chern number from quantum metric[J]. 中国物理B, 2022, 31(4): 40201-040201.
[3]	Peize Ding(丁霈泽) and Wei Yi(易为). Two-body exceptional points in open dissipative systems[J]. 中国物理B, 2022, 31(1): 10309-010309.
[4]	Hui-Qiang Liang(梁辉强) and Linhu Li(李林虎). Topological properties of non-Hermitian Creutz ladders[J]. 中国物理B, 2022, 31(1): 10310-010310.
[5]	Chao Zeng(曾超), Zhiwei Guo(郭志伟), Kejia Zhu(祝可嘉), Caifu Fan(范才富), Guo Li(李果), Jun Jiang(江俊), Yunhui Li(李云辉), Haitao Jiang(江海涛), Yaping Yang(羊亚平), Yong Sun(孙勇), and Hong Chen(陈鸿). Efficient and stable wireless power transfer based on the non-Hermitian physics[J]. 中国物理B, 2022, 31(1): 10307-010307.
[6]	Xiang-Ping Jiang(蒋相平), Yi Qiao(乔艺), and Junpeng Cao(曹俊鹏). Non-Hermitian Kitaev chain with complex periodic and quasiperiodic potentials[J]. 中国物理B, 2021, 30(7): 77101-077101.
[7]	Huiping Wang(王会平), Li Ren(任莉), Liguo Qin(秦立国), and Yueyin Qiu(邱岳寅). Edge states enhanced by long-range hopping: An analytical study[J]. 中国物理B, 2021, 30(10): 107301-107301.
[8]	柴若霖, 谢琼涛, 刘小良. Exact scattering states in one-dimensional Hermitian and non-Hermitian potentials[J]. 中国物理B, 2020, 29(9): 90301-090301.
[9]	杨毅, 蔡绍洪, 隆正文, 陈浩, 龙超云. Exact solution of the (1+2)-dimensional generalized Kemmer oscillator in the cosmic string background with the magnetic field[J]. 中国物理B, 2020, 29(7): 70302-070302.
[10]	谢琼涛, 刘小良. Exact analytical results for a two-level quantum system under a Lorentzian-shaped pulse field[J]. 中国物理B, 2020, 29(6): 60305-060305.
[11]	董晓菲, 谢幼飞, 陈庆虎. Unified approach to various quantum Rabi models witharbitrary parameters[J]. 中国物理B, 2020, 29(2): 20302-020302.
[12]	邓凤麟, 胡湘生, 王少峰. Dislocation neutralizing in a self-organized array of dislocation and anti-dislocation[J]. 中国物理B, 2019, 28(11): 116103-116103.
[13]	刘汉泽, 张丽香. Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation[J]. 中国物理B, 2018, 27(4): 40202-040202.
[14]	谭鸿威, 杨锦波, 张靖仪, 何唐梅. The global monopole spacetime and its topological charge[J]. 中国物理B, 2018, 27(3): 30401-030401.
[15]	谭志中. Recursion-transform method and potential formulae of the m×n cobweb and fan networks[J]. 中国物理B, 2017, 26(9): 90503-090503.