Exceptional rings and non-Abelian topology in non-Hermitian high-spin systems

doi:10.1088/1674-1056/addcbe

摘要/Abstract

摘要： Topological phases featuring non-Abelian charges have garnered significant attention in recent years. In parallel, the study of multiband exceptional topology in non-Hermitian systems has emerged as a prominent research direction. In this study, we investigate a parity-time (PT) symmetric Hamiltonian, which hosts both conventional non-Abelian topological phases (NATPs) and hybrid phases. We propose an experimental scheme using spin-1 atoms with spin-orbit coupling trapped in two-dimensional (2D) lattices. Before adding a non-Hermitian term, we find the emergence of distinct topological phases mixed by two NATPs and establish their connection with NATPs theory. When a non-Hermitian term that preserves PT symmetry protection was introduced, stable second-order exceptional rings and third-order exceptional points emerge and they drive the edge states to manifest as discontinuous Fermi arcs in the surface Brillouin zone. However, with the variation of the non-Hermitian term, it is rather intriguing that two types of exceptional rings here transition from being internally tangent to externally tangent, transforming into a new topological phase equivalent to the Hermitian case. This research provides deeper insights into the nature of NATPs and the topological implications of exceptional structures, contributing to the field of topological physics.

关键词: non-Abelian topology, parity-time symmetry, exceptional point, ultracold atoms

Abstract: Topological phases featuring non-Abelian charges have garnered significant attention in recent years. In parallel, the study of multiband exceptional topology in non-Hermitian systems has emerged as a prominent research direction. In this study, we investigate a parity-time (PT) symmetric Hamiltonian, which hosts both conventional non-Abelian topological phases (NATPs) and hybrid phases. We propose an experimental scheme using spin-1 atoms with spin-orbit coupling trapped in two-dimensional (2D) lattices. Before adding a non-Hermitian term, we find the emergence of distinct topological phases mixed by two NATPs and establish their connection with NATPs theory. When a non-Hermitian term that preserves PT symmetry protection was introduced, stable second-order exceptional rings and third-order exceptional points emerge and they drive the edge states to manifest as discontinuous Fermi arcs in the surface Brillouin zone. However, with the variation of the non-Hermitian term, it is rather intriguing that two types of exceptional rings here transition from being internally tangent to externally tangent, transforming into a new topological phase equivalent to the Hermitian case. This research provides deeper insights into the nature of NATPs and the topological implications of exceptional structures, contributing to the field of topological physics.

Key words: non-Abelian topology, parity-time symmetry, exceptional point, ultracold atoms

中图分类号: (Phases: geometric; dynamic or topological)

03.65.Vf

11.30.Er (Charge conjugation, parity, time reversal, and other discrete symmetries) 42.50.-p (Quantum optics) 67.85.-d (Ultracold gases, trapped gases)

Peng-Zhen Sun(孙鹏震), Zhou-Tao Lei(雷周涛), and Yuan-Gang Deng(邓元刚). Exceptional rings and non-Abelian topology in non-Hermitian high-spin systems[J]. 中国物理B, 2025, 34(11): 110303-110303.

Peng-Zhen Sun(孙鹏震), Zhou-Tao Lei(雷周涛), and Yuan-Gang Deng(邓元刚). Exceptional rings and non-Abelian topology in non-Hermitian high-spin systems[J]. Chin. Phys. B, 2025, 34(11): 110303-110303.

参考文献

[1] Zhang H, Liu C X, Qi X L, Dai X, Fang Z and Zhang S C 2009 Nat. Phys. 5 438
[2] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[3] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[4] Vergniory M G, Elcoro L, Felser C, Regnault N, Bernevig B A and Wang Z 2019 Nature 566 480
[5] Zhang T, Jiang Y, Song Z, Huang H, He Y, Fang Z, Weng H and Fang C 2019 Nature 566 475
[6] Xiao D, Chang M C and Niu Q 2010 Rev. Mod. Phys. 82 1959
[7] Chiu C K, Teo J C Y, Schnyder A P and Ryu S 2016 Rev. Mod. Phys. 88 035005
[8] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[9] Nayak C, Simon S H, Stern A, Freedman M and Das Sarma S 2008 Rev. Mod. Phys. 80 1083
[10] Lutchyn R M, Sau J D and Das Sarma S 2010 Phys. Rev. Lett. 105 077001
[11] Goldman N, Budich J C and Zoller P 2016 Nat. Phys. 12 639
[12] Song B, Zhang L, He C, Poon T F J, Hajiyev E, Zhang S, Liu X J and Jo G B 2018 Sci. Adv. 4 aao4748
[13] H M B, Boguslawski M, Barrios M, Xin L and Chapman M S 2019 Phys. Rev. Lett. 123 173202
[14] Song B, He C, Niu S, Zhang L, Ren Z, Liu X J and Jo G B 2019 Nat. Phys. 15 911
[15] Lei Z, Deng Y and Lee C 2020 Phys. Rev. A 102 013301
[16] Lei Z, Deng Y and Lee C 2022 Phys. Rev. Res. 4 033008
[17] Liang Q, Xie D, Dong Z, Li H, Li H, Gadway B, Yi W and Yan B 2022 Phys. Rev. Lett. 129 070401
[18] Leonard J, Kim S, Kwan J, Segura P, Grusdt F, Repellin C, Goldman N and Greiner M 2023 Nature 619 495
[19] Cornish S L, Tarbutt M R and Hazzard K R A 2024 Nat. Phys. 20 730
[20] Zhao E, Wang Z, He C, Poon T F J, Pak K K, Liu Y J, Ren P, Liu X J and Jo G B 2025 Nature 637 565
[21] Lu L, Joannopoulos J D and Soljaci c M 2014 Nat. Photon. 8 821
[22] Gross C and Bloch I 2017 Science 357 995
[23] Raghu S and Haldane F D M 2008 Phys. Rev. A 78 033834
[24] Cerjan A, Huang S, Wang M, Chen K P, Chong Y and Rechtsman M C 2019 Nat. Photon. 13 623
[25] Miri M A and Alu A 2019 Science 363 eaar7709
[26] Barends R, Kelly J, Megrant A, Veitia A, Sank D, Jeffrey E, White T C, Mutus J, Fowler A G, Campbell B, Chen Y, Chen Z, Chiaro B, Dunsworth A, Neill C, O’Malley P, Roushan P, Vainsencher A, Wenner J, Korotkov A N, Cleland A N and Martinis J M 2014 Nature 508 500
[27] Satzinger K J, Liu Y J and Smith A E 2021 Science 374 1237
[28] Semeghini G, Levine H, Keesling A, Ebadi S, Wang T T, Bluvstein D, Verresen R, Pichler H, Kalinowski M, Samajdar R, Omran A, Sachdev S, Vishwanath A, Greiner M, Vuletic V and Lukin M D 2021 Science 374 1242
[29] Altland A and Zirnbauer M R 1997 Phys. Rev. B 55 1142
[30] Ryu S, Schnyder A P, Furusaki A and Ludwig A W W 2010 New J. Phys. 12 065010
[31] Zhao Y X, Chen C, Sheng X L and Yang S A 2021 Phys. Rev. Lett. 126 196402
[32] Tang F, Po H C, Vishwanath A and Wan X 2019 Nature 566 486
[33] Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett. 49 405
[34] Kane C L and Mele E J 2005 Phys. Rev. Lett. 95 226801
[35] Schnyder A P, Ryu S, Furusaki A and Ludwig A W W 2008 Phys. Rev. B 78 195125
[36] Wu Q, Soluyanov A A and Bzdusek T 2019 Science 365 1273
[37] Ahn J, Park S and Yang B J 2019 Phys. Rev. X 9 021013
[38] Bouhon A, Bzdusek T and Slager R J 2020 Phys. Rev. B 102 115135
[39] Jiang B, Bouhon A, Lin Z K, Zhou X, Hou B, Li F, Slager R J and Jiang J H 2021 Nat. Phys. 17 1239
[40] Guo C X, Chen S, Ding K and Hu H 2023 Phys. Rev. Lett. 130 157201
[41] Sun X C, Wang J B, He C and Chen Y F 2024 Phys. Rev. Lett. 132 216602
[42] Unal F N, Bouhon A and Slager R J 2020 Phys. Rev. Lett. 125 053601
[43] Guo Q, Jiang T, Zhang R Y, Zhang L, Zhang Z Q, Yang B, Zhang S and Chan C T 2021 Nature 594 195
[44] Li T and Hu H 2023 Nat. Commun. 14 6418
[45] Bouhon A, Wu Q, Slager R J, Weng H, Yazyev O V and Bzdusek T 2020 Nat. Phys. 16 1137
[46] Wang K, Dutt A, Wojcik C C and Fan S 2021 Nature 598 59
[47] Hu H and Zhao E 2021 Phys. Rev. Lett. 126 010401
[48] Chen Z G, Zhang R Y, Chan C T and Ma G 2021 Nat. Phys. 18 179
[49] Patil Y S S, Holler J, Henry P A, Guria C, Zhang Y, Jiang L, Kralj N, Read N and Harris J G E 2022 Nature 607 271
[50] Rui W B, Zhao Y X and Wang Z D 2023 Phys. Rev. B 108 165105
[51] Zhang Q, Li Y, Sun H, Liu X, Zhao L, Feng X, Fan X and Qiu C 2023 Phys. Rev. Lett. 130 017201
[52] Xu S, Sun Z Z, Wang K and Li E A 2024 Nat. Phys. 20 1469
[53] Alicea J 2012 Rep. Prog. Phys. 75 076501
[54] Stern A and Lindner N H 2013 Science 339 1179
[55] Field B and Simula T 2018 Quantum Science and Technology 3 045004
[56] Ni X, He C, Sun X C, Liu X P, Lu M H, Feng L and Chen Y F 2015 New J. Phys. 17 053016
[57] Wang D, Yang B, Wang M, Zhang R Y, Li X, Zhang Z Q, Zhang S and Chan C T 2022 Phys. Rev. Lett. 129 263604
[58] Wang M, Liu S, Ma Q, Zhang R Y, Wang D, Guo Q, Yang B, Ke M, Liu Z and Chan C T 2022 Phys. Rev. Lett. 128 246601
[59] Hu Y, Tong M, Jiang T, Jiang J H, Chen H and Yang Y 2024 Nat. Commun. 15 10036
[60] Bender C M and Boettcher S 1998 Phys. Rev. Lett. 80 5243
[61] Mostafazadeh A 2002 J. Math. Phys. 43 205
[62] Feng L, El-Ganainy R and Ge L 2017 Nat. Photon. 11 752
[63] El-Ganainy R, Makris K G, Khajavikhan M, Musslimani Z H, Rotter S and Christodoulides D N 2018 Nat. Phys. 14 11
[64] Heiss W D 2004 J. Phys. A: Math. Gen. 37 2455
[65] Dembowski C, Dietz B, Graf H D, Harney H L, Heine A, Heiss W D and Richter A 2004 Phys. Rev. E 69 056216
[66] Hassan A U, Zhen B, Soljacic M, Khajavikhan M and Christodoulides D N 2017 Phys. Rev. Lett. 118 093002
[67] Budich J C, Carlstrom J, Kunst F K and Bergholtz E J 2019 Phys. Rev. B 99 041406
[68] Zhou H and Lee J Y 2019 Phys. Rev. B 99 235112
[69] Yoshida T, Peters R, Kawakami N and Hatsugai Y 2019 Phys. Rev. B 99 121101
[70] Okugawa R and Yokoyama T 2019 Phys. Rev. B 99 041202
[71] Tang W, Jiang X, Ding K, Xiao Y X, Zhang Z Q, Chan C T and Ma G 2020 Science 370 1077
[72] Liu W, Wu Y, Duan C K, Rong X and Du J 2021 Phys. Rev. Lett. 126 170506
[73] Cayao J and Black-Schaffer A M 2023 Phys. Rev. B 107 104515
[74] Wang K, Xiao L, Lin H, Yi W, Bergholtz E J and Xue P 2023 Sci. Adv. 9 2375
[75] Wu Y, Wang Y, Ye X, Liu W, Niu Z, Duan C K, Wang Y, Rong X and Du J 2024 Nat. Nanotechnol. 19 160
[76] Xu Y, Wang S T and Duan L M 2017 Phys. Rev. Lett. 118 045701
[77] Holler J, Read N and Harris J G E 2020 Phys. Rev. A 102 032216
[78] Delplace P, Yoshida T and Hatsugai Y 2021 Phys. Rev. Lett. 127 186602
[79] Tang W, Ding K and Ma G 2023 Nat. Commun. 14 6660
[80] Montag A and Kunst F K 2024 Phys. Rev. Res. 6 023205
[81] Rotter I 2009 J. Phys. A: Math. Theor. 42 153001
[82] Lee T E 2016 Phys. Rev. Lett. 116 133903
[83] Leykam D, Bliokh K Y, Huang C, Chong Y D and Nori F 2017 Phys. Rev. Lett. 118 040401
[84] Gong Z, Ashida Y, Kawabata K, Takasan K, Higashikawa S and Ueda M 2018 Phys. Rev. X 8 031079
[85] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[86] Lee C H, Li L and Gong J 2019 Phys. Rev. Lett. 123 016805
[87] Kawabata K, Sato M and Shiozaki K 2020 Phys. Rev. B 102 205118
[88] Zhang K, Yang Z and Fang C 2020 Phys. Rev. Lett. 125 126402
[89] Okuma N, Kawabata K, Shiozaki K and Sato M 2020 Phys. Rev. Lett. 124 086801
[90] Li Y, Liang C, Wang C, Lu C and Liu Y C 2022 Phys. Rev. Lett. 128 223903
[91] Zhu P, Sun X Q, Hughes T L and Bahl G 2023 Nat. Commun. 14 720
[92] Schindler F, Gu K, Lian B and Kawabata K 2023 PRX Quantum 4 030315
[93] Lin R, Tai T, Li L and Lee C H 2023 Front. Phys. 18 53605
[94] Ma X R, Cao K, Wang X R, Wei Z, Du Q and Kou S P 2024 Phys. Rev. Res. 6 013213
[95] Lei Z, Lee C H and Li L 2024 Commun. Phys. 7 100
[96] Luo X W, Sun K and Zhang C 2017 Phys. Rev. Lett. 119 193001
[97] Hu H, Hou J, Zhang F and Zhang C 2018 Phys. Rev. Lett. 120 240401
[98] Li D, Huang L, Peng P, Bian G, Wang P, Meng Z, Chen L and Zhang J 2020 Phys. Rev. A 102 013309
[99] Zhang M, Yuan X, Li Y, Luo X W, Liu C, Zhu M, Qin X, Zhang C, Lin Y and Du J 2022 Phys. Rev. Lett. 129 250501