Please wait a minute...
Chin. Phys. B, 2023, Vol. 32(8): 080304    DOI: 10.1088/1674-1056/acd0a5
GENERAL Prev   Next  

Exact solution of slow quench dynamics and nonadiabatic characterization of topological phases

Rui Wu(邬睿), Panpan Fang(房盼攀), Chen Sun(孙辰), and Fuxiang Li(李福祥)
School of Physics and Electronics, Hunan University, Changsha 410082, China
Abstract  Previous studies have shown that the bulk topology of single-particle systems can be captured by the band inversion surface or by the spin inversion surface emerging on the time-averaged spin polarization. Most of the studies, however, are based on the single-particle picture even though the systems are fermionic and multi-bands. Here, we study the slow quench dynamics of topological systems with all the valence bands fully occupied, and show that the concepts of band inversion surface and spin inversion surface are still valid. More importantly, the many-particle nonadiabatic quench dynamics is shown to be reduced to a new and nontrivial three-level Landau-Zener model. This nontrivial three-level Landau-Zener problem is then solved analytically by applying the integrability condition and symmetry considerations, and thus adds a new member to the few models that are exactly solvable. Based on the analytical results, the topological spin texture revealed by the time-averaged spin polarization can be applied to characterize the bulk topology and thus provides a direct comparison for future experiments.
Keywords:  Landau-Zener      slow quench      nonadiabatic  
Received:  07 January 2023      Revised:  23 April 2023      Accepted manuscript online:  27 April 2023
PACS:  03.65.Vf (Phases: geometric; dynamic or topological)  
  33.50.Hv (Radiationless transitions, quenching)  
  71.70.Di (Landau levels)  
Fund: Project supported by the National Key Research and Development Program of China (Grant No.2021YFA1200700), the National Natural Science Foundation of China (Grant Nos.11905054, 12275075 and 12105094), and the Fundamental Research Funds for the Central Universities of China.
Corresponding Authors:  Fuxiang Li     E-mail:  fuxiangli@hnu.edu.cn

Cite this article: 

Rui Wu(邬睿), Panpan Fang(房盼攀), Chen Sun(孙辰), and Fuxiang Li(李福祥) Exact solution of slow quench dynamics and nonadiabatic characterization of topological phases 2023 Chin. Phys. B 32 080304

[1] Klitzing K V, Dorda G and Pepper M 1980 Phys. Rev. Lett. 45 494
[2] Laughlin R B 1981 Phys. Rev. B 23 5632
[3] Halperin B I 1982 Phys. Rev. B 25 2185
[4] Haldane F D M 1988 Phys. Rev. Lett. 61 2015
[5] Bernevig B A, Hughes T L and Zhang S C 2006 Science 314 1757
[6] Haldane F D M and Raghu S 2008 Phys. Rev. Lett. 100 013904
[7] Khanikaev A B, Mousavi S H, Tse W K, Kargarian M, MacDonald A H and Shvets G 2013 Nat. Mater. 12 233
[8] Thouless D J, Kohmoto M, Nightingale M P and den Nijs M 1982 Phys. Rev. Lett. 49 405
[9] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[10] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[11] Aidelsburger M, Atala M, Lohse M, Barreiro J T, Paredes B and Bloch I 2013 Phys. Rev. Lett. 111 185301
[12] Miyake H, Siviloglou G A, Kennedy C J, Burton W C and Ketterle W 2013 Phys. Rev. Lett. 111 185302
[13] Aidelsburger M, Lohse M, Schweizer C, Atala M, Barreiro J T, Nascimbne S, Cooper N R, Bloch I and Goldman N 2015 Nat. Phys. 11 162
[14] Eisert J, Friesdorf M and Gogolin C 2015 Nat. Phys. 11 124
[15] Wang Z Y, Cheng X C, Wang B Z, Zhang J Y, Lu Y H, Yi C R, Niu S, Deng Y J, Liu X J, Chen S and Pan J W 2021 Science 372 271
[16] McGinley M and Cooper N R 2019 Phys. Rev. B 99 075148
[17] Heyl M, Polkovnikov A and Kehrein S 2013 Phys. Rev. Lett. 110 135704
[18] Heyl M 2014 Phys. Rev. Lett. 113 205701
[19] Zunkovic B, Heyl M, Knap M and Silva A 2018 Phys. Rev. Lett. 120 130601
[20] Corps A L and Relano A 2023 Phys. Rev. Lett. 130 100402
[21] Pastori L, Barbarino S and Budich J C 2020 Phys. Rev. Res. 2 033259
[22] Lee T E, Reiter F and Moiseyev N 2014 Phys. Rev. Lett. 113 250401
[23] Zhu B, Ke Y G, Zhong H H and Lee C H 2020 Phys. Rev. Res. 2 023043
[24] Zhang L, Zhang L, Niu S and Liu X J 2018 Sci. Bull. 63 1385
[25] Sun W, Yi C R, Wang B Z, Zhang W W, Sanders B C, Xu X T, Wang Z Y, Schmiedmayer J, Deng Y J, Liu X J, Chen S and Pan J W 2018 Phys. Rev. Lett. 121 250403
[26] Yi C R, Zhang L, Zhang L, Jiao R H, Cheng X C, Wang Z Y, Xu X T, Sun W, Liu X J, Chen S and Pan J W 2019 Phys. Rev. Lett. 123 190603
[27] Wang Y, Ji W T, Chai Z H, Guo Y H, Wang M Q, Ye X Y, Yu P, Zhang L, Qin X, Wang P F, Shi F Z, Rong X, Lu D W, Liu X J and Du J F 2019 Phys. Rev. A 100 052328
[28] Liu X J, Liu Z X and Cheng M 2013 Phys. Rev. Lett. 110 076401
[29] Liu X J, Law K T and Ng T K 2014 Phys. Rev. Lett. 112 086401
[30] Bayat A, Alkurtass B, Sodano P, Johannesson H and Bose S 2018 Phys. Rev. Lett. 121 030601
[31] Zhang L, Zhang L, Hu Y, Niu S and Liu X J 2021 Phys. Rev. B 103 224308
[32] Ye J C and Li F X 2020 Phys. Rev. A 102 042209
[33] Fang P, Wang Y X and Li F 2022 Phys. Rev. A 106 022219
[34] Landau L D and Lifshitz E M 1980 Quantum Mechanics (Oxford: Butterworth-Heinemann)
[35] Sinitsyn N A 2014 Phys. Rev. A 90 062509
[36] Sinitsyn N A, Yuzbashyan E A, Chernyak V Y, Patra A and Sun C 2018 Phys. Rev. Lett. 120 190402
[37] Sinitsyn N A and Li F 2016 Phys. Rev. A 93 063859
[38] Zhang L, Jia W and Liu X J 2022 Sci. Bull. 67 1236
[39] Yu L X, Ji T W, Zhang L, Wang Y, Wu J S and Liu X J 2021 Phys. Rev. X Quantum 2 020320
[49] Li F, Sun C, Chernyak V Y and Sinitsyn N A 2017 Phys. Rev. A 96 022107
[40] del Campo A, Kibble T W and Zurek W H 2013 J. Phys. Condens. Matter 25 404210
[41] Farhi E, Goldstone J, Gutmann S, Lapan J, Ludgren A and Preda D 2001 Science 292 472
[42] Demkov Y N and Ostrovsky V N 2001 J. Phys. B 34 2419
[43] Sinitsyn N A and Li F 2016 Phys. Rev. A 93 063859
[44] Schnyder A P, Ryu S, Furusaki A and Ludwig A W W 2008 Phys. Rev. B 78 195125
[45] Sinitsyn N A, Lin J and Chernyak V Y 2017 Phys. Rev. A 95 012140
[46] Sinitsyn N A 2014 Phys. Rev. A 90 062509
[47] Fu L and Kane C L 2006 Phys. Rev. B 74 195312
[48] Fu L and Kane C L 2007 Phys. Rev. B 76 045302
[50] Rachel S and Le H K 2010 Phys. Rev. B 82 075106
[51] Hohenadler M, Lang T C and Assaad F F 2011 Phys. Rev. Lett. 106 100403
[1] Nonadiabatic geometric phase in a doubly driven two-level system
Weixin Liu(刘伟新), Tao Wang(汪涛), and Weidong Li(李卫东). Chin. Phys. B, 2023, 32(5): 050311.
[2] Effect of conical intersection of benzene on non-adiabatic dynamics
Duo-Duo Li(李多多) and Song Zhang(张嵩). Chin. Phys. B, 2022, 31(8): 083103.
[3] Phase-sensitive Landau-Zener-Stückelberg interference in superconducting quantum circuit
Zhi-Xuan Yang(杨智璇), Yi-Meng Zhang(张一萌), Yu-Xuan Zhou(周宇轩), Li-Bo Zhang(张礼博), Fei Yan(燕飞), Song Liu(刘松), Yuan Xu(徐源), and Jian Li(李剑). Chin. Phys. B, 2021, 30(2): 024212.
[4] Quench dynamics in 1D model with 3rd-nearest-neighbor hoppings
Shuai Yue(岳帅), Xiang-Fa Zhou(周祥发), and Zheng-Wei Zhou(周正威). Chin. Phys. B, 2021, 30(2): 026402.
[5] Cluster mean-field study of spinor Bose-Hubbard ladder: Ground-state phase diagram and many-body population dynamics
Li Zhang(张莉), Wenjie Liu(柳文洁), Jiahao Huang(黄嘉豪), and Chaohong Lee(李朝红). Chin. Phys. B, 2021, 30(2): 026701.
[6] Collapses-revivals phenomena induced by weak magnetic flux in diamond chain
Na-Na Chang(常娜娜), Wen-Quan Jing(景文泉), Yu Zhang(张钰), Ai-Xia Zhang(张爱霞), Ju-Kui Xue(薛具奎), Su-Peng Kou(寇谡鹏). Chin. Phys. B, 2020, 29(1): 010306.
[7] Tunneling dynamics of bosons in the diamond lattice chain
Na-Na Chang(常娜娜), Ju-Kui Xue(薛具奎). Chin. Phys. B, 2018, 27(10): 105203.
[8] Macroscopic resonant tunneling in an rf-SQUID flux qubit under a single-cycle sinusoidal driving
Jianxin Shi(史建新), Weiwei Xu(许伟伟), Guozhu Sun(孙国柱), Jian Chen(陈健), Lin Kang(康琳), Peiheng Wu(吴培亨). Chin. Phys. B, 2017, 26(4): 047402.
[9] Nonadiabatic dynamics of electron injection into organic molecules
Zhu Li-Ping(朱丽萍), Qiu Yu(邱宇), and Tong Guo-Ping(童国平) . Chin. Phys. B, 2012, 21(7): 077302.
[10] Linear and nonlinear excitations in complex plasmas with nonadiabatic dust charge fluctuation and dust size distribution
Zhang Li-Ping(张丽萍), Xue Ju-Kui(薛具奎), and Li Yan-Long(李延龙) . Chin. Phys. B, 2011, 20(11): 115201.
[11] The second dissociation threshold bound levels of hydrogen molecule
Zhang Yan-Peng(张彦鹏), Song Jian-Ping(宋建平), Gan Chen-Li(甘琛利), Yan Xiang-An(严祥安), Nie Zhi-Qiang(聂志强), Jiang Tong(姜彤), Li Ling(李岭), Du Kai(杜凯), Zhang Xiang-Chen(张相臣), Lu Ke-Qing(卢克清), and E.E. Eyler. Chin. Phys. B, 2006, 15(10): 2288-2296.
[12] The instability of electrostatic wave in a magnetized dusty plasma with nonadiabatic dust charge fluctuation
Zhang Li-Ping (张丽萍), Xue Ju-Kui (薛具奎). Chin. Phys. B, 2005, 14(10): 2052-2060.
No Suggested Reading articles found!