Real non-Hermitian energy spectra without any symmetry

doi:10.1088/1674-1056/ac67c6

中国物理B ›› 2022, Vol. 31 ›› Issue (7): 70308-070308.doi: 10.1088/1674-1056/ac67c6

所属专题： SPECIAL TOPIC — Non-Hermitian physics

Real non-Hermitian energy spectra without any symmetry

Boxue Zhang(张博学)^1,†, Qingya Li(李青铔)^2,†, Xiao Zhang(张笑)¹, and Ching Hua Lee(李庆华)^2,‡

1 School of Physics, Sun Yat-sen University, Guangzhou 510275, China;
2 Department of Physics, National University of Singapore, Singapore 117542, Singapore

收稿日期:2022-03-04 修回日期:2022-04-05 接受日期:2022-04-18 出版日期:2022-06-09 发布日期:2022-06-18
通讯作者: Ching Hua Lee E-mail:phylch@nus.edu.sg
基金资助:
X.Z. is supported by the National Natural Science Foundation of China (Grant No. 11874431), the National Key R&D Program of China (Grant No. 2018YFA0306800), and the Guangdong Science and Technology Innovation Youth Talent Program (Grant No. 2016TQ03X688).

Real non-Hermitian energy spectra without any symmetry

Boxue Zhang(张博学)^1,†, Qingya Li(李青铔)^2,†, Xiao Zhang(张笑)¹, and Ching Hua Lee(李庆华)^2,‡

1 School of Physics, Sun Yat-sen University, Guangzhou 510275, China;
2 Department of Physics, National University of Singapore, Singapore 117542, Singapore

Received:2022-03-04 Revised:2022-04-05 Accepted:2022-04-18 Online:2022-06-09 Published:2022-06-18
Contact: Ching Hua Lee E-mail:phylch@nus.edu.sg
Supported by:
X.Z. is supported by the National Natural Science Foundation of China (Grant No. 11874431), the National Key R&D Program of China (Grant No. 2018YFA0306800), and the Guangdong Science and Technology Innovation Youth Talent Program (Grant No. 2016TQ03X688).

1. 附件.pdf(2887KB)

摘要/Abstract

摘要： Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic non-Hermitian phenomena. In this work, we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability. We showcase, for different classes of energy dispersions, various ansatz models that possess large parameter space regions with real spectra, despite not having any obvious symmetry. These minimal local models can be quickly implemented in non-reciprocal experimental setups such as electrical circuits with operational amplifiers.

关键词: non-Hermitian physics, real energy spectra, non-Hermitian skin effect

Abstract: Non-Hermitian models with real eigenenergies are highly desirable for their stability. Yet, most of the currently known ones are constrained by symmetries such as PT-symmetry, which is incompatible with realizing some of the most exotic non-Hermitian phenomena. In this work, we investigate how the non-Hermitian skin effect provides an alternative route towards enforcing real spectra and system stability. We showcase, for different classes of energy dispersions, various ansatz models that possess large parameter space regions with real spectra, despite not having any obvious symmetry. These minimal local models can be quickly implemented in non-reciprocal experimental setups such as electrical circuits with operational amplifiers.

Key words: non-Hermitian physics, real energy spectra, non-Hermitian skin effect

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

03.65.Yz

03.65.Vf (Phases: geometric; dynamic or topological) 03.65.-w (Quantum mechanics)

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.

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]. Chin. Phys. B, 2022, 31(7): 70308-070308.

参考文献

[1] Kawabata K, Shiozaki K, Ueda M and Sato M 2019 Phys. Rev. X 9 041015
[2] Liu C H, Jiang H and Chen S 2019 Phys. Rev. B 99 125103
[3] Bergholtz E J, Budich J C and Kunst F K 2021 Rev. Mod. Phys. 93 015005
[4] Sayyad S, Yu J, Grushin A G and Sieberer L M 2021 Phys. Rev. Res. 3 033022
[5] Wojcik C C, Wang K, Dutt A, Zhong J and Fan S 2021 arXiv preprint arXiv:2111.09977
[6] Shiozaki K and Ono S 2021 Phys. Rev. B 104 035424
[7] Borgnia D S, Kruchkov A J and Slager R J 2020 Phys. Rev. Lett. 124 056802
[8] Park H, Gao W, Zhang X and Oh S S 2022 Nanophotonics
[9] Chen W, Özdemir Ş, Zhao G, Wiersig J and Yang L 2017 Nature 548 192
[10] Wiersig J 2014 Phys. Rev. Lett. 112 203901
[11] Zhang M, Sweeney W, Hsu C W, Yang L, Stone A D and Jiang L 2019 Phys. Rev. Lett. 123 180501
[12] Zeng C, Sun Y, Li G, Li Y, Jiang H, Yang Y and Chen H 2019 Opt. Express 27 27562
[13] Budich J C and Bergholtz E J 2020 Phys. Rev. Lett. 125 180403
[14] Sahoo A and Sarma A K 2022 arXiv preprint arXiv:2202.07972
[15] Hodaei H, Hassan A U, Wittek S, Garcia-Gracia H, El-Ganainy R, Christodoulides D N and Khajavikhan M 2017 Nature 548 187
[16] Li L, Mu S, Lee C H and Gong J 2021 Nat. Commun. 12 5294
[17] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[18] Yang Z, Zhang K, Fang C and Hu J 2020 Phys. Rev. Lett. 125 226402
[19] Yokomizo K and Murakami S 2019 Phys. Rev. Lett. 123 066404
[20] Helbig T, Hofmann T, Imhof S, Abdelghany M, Kiessling T, Molenkamp L, Lee C, Szameit A, Greiter M and Thomale R 2020 Nat. Phys. 16 747
[21] Yao S, Song F and Wang Z 2018 Phys. Rev. Lett. 121 136802
[22] Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402
[23] Guo G F, Bao X X and Tan L 2021 arXiv preprint arXiv:2106.06384
[24] Bartlett J, Hu H and Zhao E 2021 Phys. Rev. B 104 195131
[25] Zhang Z Q, Liu H, Liu H, Jiang H and Xie X C 2022 arXiv preprint arXiv:2201.01577
[26] Cao Y, Li Y and Yang X 2021 Phys. Rev. B 103 075126
[27] Jin L and Song Z 2019 Phys. Rev. B 99 081103
[28] Kunst F K, Edvardsson E, Budich J C and Bergholtz E J 2018 Phys. Rev. Lett. 121 026808
[29] Koch R and Budich J C 2020 Eur. Phys. J. D 74 70
[30] Imura K I and Takane Y 2020 Prog. Theor. Exp. Phys. 2020 12A103
[31] Qin F, Shen R and Lee C H 2022 arXiv preprint arXiv:2202.10481
[32] Jiang H and Lee C H Jiang H and Lee C H 2022 Chin. Phys. B 31 050307
[33] Li L, Lee C H, Mu S and Gong J 2020 Nat. Commun. 11 5491
[34] Lee C H 2022 Phys. Rev. Lett. 128 010402
[35] Chen W, Peng L, Lu H and Lu X 2022 Phys. Rev. B 105 075126
[36] Chang P Y, You J S, Wen X and Ryu S 2020 Phys. Rev. Res. 2 033069
[37] Zhou B, Wang R and Wang B 2020 Phys. Rev. B 102 205116
[38] Yokomizo K and Murakami S 2021 Phys. Rev. B 104 165117
[39] Pan J S, Li L and Gong J 2021 Phys. Rev. B 103 205425
[40] Lee C H and Longhi S 2020 Commun. Phys. 3 147
[41] Zhou L, Gu Y and Gong J 2021 Phys. Rev. B 103 L041404
[42] Lv C, Zhang R, Zhai Z and Zhou Q 2021 arXiv preprint arXiv:2106.02477
[43] Stålhammar M, Larana-Aragon J, Rødland L and Kunst F K 2022 arXiv preprint arXiv:2106.05030
[44] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[45] El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S and Christodoulides D N 2018 Nat. Phys. 14 11
[46] Stegmaier A, Imhof S, Helbig T, Hofmann T, Lee C H, Kremer M, Fritzsche A, Feichtner T, Klembt S, Höfling S, et al. 2021 Phys. Rev. Lett. 126 215302
[47] Fring A 2022 arXiv preprint arXiv:2201.05140
[48] Xiao L, Deng T, Wang K, Wang Z, Yi W and Xue P 2021 Phys. Rev. Lett. 126 230402
[49] Schomerus H 2013 Opt. Lett. 38 1912
[50] Weimann S, Kremer M, Plotnik Y, Lumer Y, Nolte S, Makris K, Segev M, Rechtsman M C and Szameit A 2016 Nat. Mater. 16 433
[51] Özdemir Ş K, Rotter S, Nori F and Yang L 2019 Nat. Mater. 18 783
[52] Bendix O, Fleischmann R, Kottos T and Shapiro B 2009 Phys. Rev. Lett. 103 030402
[53] Ghatak A, Brandenbourger M, van Wezel J and Coulais C 2020 Proc. Natl. Acad. Sci. USA 117 29561
[54] Xiao L, Deng T, Wang K, Zhu G, Wang Z, Yi W and Xue P 2020 Nat. Phys. 16 761
[55] Bouganne R, Aguilera M B, Ghermaoui A, Beugnon J and Gerbier F 2020 Nat. Phys. 16 21
[56] Song W, Sun W, Chen C, Song Q, Xiao S, Zhu S and Li T 2019 Phys. Rev. Lett. 123 165701
[57] Hou J, Li Z, Luo X W, Gu Q and Zhang C 2020 Phys. Rev. Lett. 124 073603
[58] Longhi S 2018 arXiv preprint arXiv:1802.05025
[59] Ningyuan J, Owens C, Sommer A, Schuster D and Simon J 2015 Phys. Rev. X 5 021031
[60] Scheibner C, Irvine W T M and Vitelli V 2020 Phys. Rev. Lett. 125 118001
[61] Zeng Q B 2021 arXiv preprint arXiv:2110.06597
[62] Long Y, Xue H and Zhang B 2021 arXiv preprint arXiv:2111.02701
[63] Kawabata K and Sato M 2020 Phys. Rev. Res. 2 033391
[64] Aharonov Y, Massar S, Popescu S, Tollaksen J and Vaidman L 1996 Phys. Rev. Lett. 77 983
[65] Nirala G, Sahoo S N, Pati A K and Sinha U 2019 Phys. Rev. A 99 022111
[66] Li J X, Chang S L, Zhao Y H, Xiao X and Leng Y 2021 Laser Physics 31 095202
[67] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401
[68] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801
[69] Longhi S 2021 Phys. Rev. B 104 125109
[70] Peng Y, Jie J, Yu D and Wang Y 2022 arXiv preprint arXiv:2201.10318
[71] Liang Q, Xie D, Dong Z, Li H, Li H, Gadway B, Yi W and Yan B 2022 arXiv preprint arXiv:2201.09478
[72] Zhu X, Wang H, Gupta S K, Zhang H, Xie B, Lu M and Chen Y 2020 Phys. Rev. Res. 2 013280
[73] Guo C X, Liu C H, Zhao X M, Liu Y and Chen S 2021 Phys. Rev. Lett. 127 116801
[74] Lee C H, Li L, Thomale R and Gong J 2020 Phys. Rev. B 102 085151
[75] Qi X L 2013 arXiv preprint arXiv:1309.6282
[76] Gu Y, Lee C H, Wen X, Cho G Y, Ryu S and Qi X L 2016 Phys. Rev. B 94 125107
[77] As we interpolate between OBCs and PBCs, we observe a peculiar scaling behavior of the corresponding effective κ.[98]
[78] Guo G F, Bao X X and Tan L 2021 New J. Phys. 23 123007
[79] However, the topological eigenenergies themselves fall outside of the purview of our prescription, because they are isolated solutions that are not adiabatically connected to any Bloch solution.
[80] Ghatak A and Das T 2019 J. Phys:Condens. Mat. 31 263001
[81] Song F, Yao S and Wang Z 2019 Phys. Rev. Lett. 123 246801
[82] Liu H, Zhou J K, Wu B L, Zhang Z Q and Jiang H 2021 Phys. Rev. B 103 224203
[83] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079
[84] Zhang S B, Denner M M, Bzdušek T, Sentef M A and Neupert T 2022 arXiv preprint arXiv:2201.12653
[85] Tai T and Lee C H 2022 arXiv preprint arXiv:2202.03462
[86] Lee C H and Thomale R 2019 Phys. Rev. B 99 201103
[87] Longhi S 2020 Phys. Rev. Lett. 124 066602
[88] Martinez Alvarez V M, Barrios Vargas J E and Foa Torres L E F 2018 Phys. Rev. B 97 121401
[89] Yang R, Tan J W, Tai T, Koh J M, Li L, Longhi S and Lee C H 2022 arXiv preprint arXiv:2201.04153
[90] Li L and Lee C H 2022 Science Bulletin 67 685
[91] Shen R and Lee C H 2021 arXiv preprint arXiv:2107.03414
[92] Tahir-Kheli J and Goddard III W A 2011 The Journal of Physical Chemistry Letters 2 2326
[93] Budich J C and Bergholtz E J 2020 Phys. Rev. Lett. 125 180403
[94] Yang X, Li J, Ding Y, Xu M, Zhu X F and Zhu J 2022 Phys. Rev. Lett. 128 065701
[95] Hofmann T, Helbig T, Lee C H, Greiter M and Thomale R 2019 Phys. Rev. Lett. 122 247702
[96] Zou D, Chen T, He W, Bao J, Lee C H, Sun H and Zhang X 2021 Nat. Commun. 12 7201
[97] Blais A, Grimsmo A L, Girvin S M and Wallraff A 2021 Rev. Mod. Phys. 93 025005
[98] Li L, Lee C H and Gong J 2021 Commun. Phys. 4 42
[99] Li L, Lee C H, Mu S and Gong J 2020 Nat. Commun. 11 5491
[100] Liu C H, Zhang K, Yang Z and Chen S 2020 Phys. Rev. Res. 2 043167
[101] Rafi-Ul-Islam S, Siu Z B, Sahin H, Lee C H and Jalil M 2021 arXiv preprint arXiv:2108.02457

Real non-Hermitian energy spectra without any symmetry

Real non-Hermitian energy spectra without any symmetry

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