Phase diagram and quench dynamics of a periodically driven Haldane model

doi:10.1088/1674-1056/ad4eb3

Abstract We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function. By using the Floquet theory, we obtain the topological phase diagram of the system. We also find that anomalous Floquet topological phases exist in the system. Focusing on examining the quench dynamics among topological phases, we analyze the site distribution of the $0$-mode and $\pi$-mode edge states in long-period evolution after a quench. The results demonstrate that, under certain conditions, the site distribution of the $0$-mode can be confined at the edge even in long-period evolution. Additionally, both the $0$-mode and $\pi$-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters $\left( T,\frac{M_2}{M_1} \right) $ in the phase diagram cross away from the phase boundary $\frac{M_2}{M_1}=\frac{6\sqrt{3} t_2}{M_1}-1$. Furthermore, we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench. Our findings reveal some new characteristics of quench dynamics in a periodically driven system.

Keywords: Floquet system Haldane model quench dynamics topological phase diagram

Received: 14 March 2024
Revised: 14 May 2024
Accepted manuscript online: 22 May 2024

PACS:	03.65.Vf	(Phases: geometric; dynamic or topological)
	03.65.Ge	(Solutions of wave equations: bound states)

Fund: We thank Ping Fang, Jieyun Yan, and Yueheng Lan for inspiring discussions. The project was supported by the National Natural Science Foundation of China (Grant No. 12004049).

Corresponding Authors: Minxuan Ren
E-mail: renminxuanphy@bupt.edu.cn

Cite this article:

Minxuan Ren(任民烜), Han Yang(杨焓), and Mingyuan Sun(孙明远) Phase diagram and quench dynamics of a periodically driven Haldane model 2024 Chin. Phys. B 33 090309

[1] Thouless D J, Kohmoto M, Nightingale M P and Nijs M den 1982 Phys. Rev. Lett. 49 405
[2] Wen X G 1990 Int. J. Mod. Phys. B 04 239
[3] Hasan M Z and Kane C L 2010 Rev. Mod. Phys. 82 3045
[4] Qi X L and Zhang S C 2011 Rev. Mod. Phys. 83 1057
[5] Rudner M S, Lindner N H, Berg E and Levin M 2013 Phys. Rev. X 3 031005
[6] Rudner M S and Lindner N H 2020 Nat. Rev. Phys. 2 229
[7] Lee T E 2015 Phys. Rev. Lett. 116 133903
[8] Yao S and Wang Z 2018 Phys. Rev. Lett. 121 086803
[9] Xu Q Y, Liu F, Chen C Z and Xu D H 2020 Phys. Rev. B 105 075411
[10] Zhou L and Gong J 2018 Phys. Rev. B 98 205417
[11] Wu H and An J H 2020 Phys. Rev. B 102 041119
[12] Kitagawa T, Berg E, Rudner M and Demler E 2010 Phys. Rev. B 82 235114
[13] Else D V and Nayak C 2016 Phys. Rev. B 93 201103
[14] Zhou L, Wang H, Ho D Y H and Gong J 2014 Eur. Phys. J. B 87 204
[15] Zhou L and Du Q 2021 J. Phys.: Condens. Matter 33 345403
[16] Luan L N, Zhang M Y, Wang L C 2023 Chin. Phys. B 32 090302
[17] Bukov M, Gopalakrishnan S, Knap M and Demler E 2015 Phys. Rev. Lett. 115 205301
[18] Seetharam K I, Bardyn C E, Lindner N H, Rudner M S and Refael J 2019 Phys. Rev. B 99 014307
[19] Ikeda T N and Sato M 2020 Sci. Adv. 6 27
[20] Cheng Z and Potter A C 2022 Phys. Rev. B 106 L220307
[21] Fazzini S, Chudzinski P, Dauer C, Schneider I and Eggert S 2021 Phys. Rev. Lett. 126 243401
[22] Eckardt A 2015 Rev. Mod. Phys. 89 011004
[23] Price H M, Ozawa T and Goldman N 2017 Phys. Rev. A 95 023607
[24] Lin Y J, Jiménez-García K and Spielman I B 2011 Nature 471 83
[25] Huang L, Meng Z, Wang P, Peng P, Zhang S L, Chen L, Li D, Zhou Q and Zhang J 2016 Nat. Phys. 12 540
[26] Wu Z, Zhang L, Sun W, Xu X T, Wang B Z, Ji S C, Deng Y, Chen S, Liu X J and Pan J W 2016 Science 354 6308
[27] Chen H R, Lin K Y, Chen P K, Chiu N C, Wang J B, Huang P, Yip S K, Kawaguchi Y and Lin Y J 2018 Phys. Rev. Lett. 121 113204
[28] Luo X W, Zhou X, Li C F, Xu J S, Guo G C and Zhou Z W 2015 Nat. Commun. 6 7704
[29] Zhang X, Jiang W, Deng J, Wang K, Chen J, Zhang P, Ren W, Dong H, Xu S, Gao Y, Jin J, Zhu X, Guo Q, Li H, Song C, Gorshkov A V, Iadecola T, Liu F, Gong Z X, Wang Z, Deng D L and Wang H 2022 Nature 607 468
[30] Jünemann J, Piga A, Ran S J, Lewenstein M, Rizzi M and Bermudez A 2016 Phys. Rev. X 7 031057
[31] Potirniche I D, Potter A C, Schleier-Smith M, Vishwanath A and Yao N Y 2017 Phys. Rev. Lett. 119 123601
[32] Liu X J, Law K T, Ng T K and Lee Patrick A 2013 Phys. Rev. Lett. 111 120402
[33] Peng Y G, Qin C Z, Zhao D G, Shen Y X, Xu X Y, Bao M, Jia H and Zhu X F 2016 Nat. Commun. 7 13368
[34] Mukherjee S, Spracklen A, Valiente M, Andersson E, Öhberg P, Gold-man N and Thomson R R 2017 Nat. Commun. 8 13918
[35] Maczewsky L J, Zeuner J M, Nolte S and Szameit A 2017 Nat. Commun. 8 13756
[36] Wintersperger K, Braun C, Ünal F N, Eckardt A, Liberto D M, Gold-man N, Block I and Aidelsburger M 2020 Nat. Phys. 16 1058
[37] Zhang L, Zhang L, Niu S and Liu X J 2018 Sci. Bull. 63 1385
[38] Zhang L, Zhang L and Liu X J 2020 Phys. Rev. Lett. 125 183001
[39] Zhang J Y, Yi C R, Zhang L, Jiao R H, Shi Y K, Yuan H, Zhang W, Liu X J, Chen S and Pan J W 2023 Phys. Rev. Lett. 130 043201
[40] Zhang L and Liu X J 2022 PRX Quantum 3 040312
[41] Barkeshli M and Qi X L 2012 Phys. Rev. X 2 031013
[42] Wang Y F, Yao H and Gong C D 2012 Phys. Rev. B 86 201101
[43] Wang J, Lian B, Zhang H, Xu Y and Zhang S C 2013 Phys. Rev. Lett 111 136801
[44] Skirlo S A, Lu L, Igarashi Y, Yan Q, Joannopoulos J and Soljai M 2015 Phys. Rev. Lett 115 253901
[45] Xiong T S, Gong J and An J H 2016 Phys. Rev. B 93 184306
[46] Yang K, Xu S, Zhou L, Zhao Z, Xie T, Ding Z, Ma W, Gong J, Shi F and Du J 2022 Phys. Rev. B 106 184106
[47] Haldane F D M 1988 Phys. Rev. Lett 61 2015
[48] Wright A R 2013 Sci. Rep. 3 2736
[49] Garrity K F and Vanderbilt D 2014 Phys. Rev. B 90 121103
[50] Jotzu G, Messer M, Desbuquois R, Lebrat M, Uehlinger T, Greif D and Esslinger T 2014 Nature 515 237
[51] Ding Y, Peng Y, Zhu Y, Fan X, Yang J, Liang B, Zhu X, Wan X and Cheng J 2017 Phys. Rev. Lett 122 014302
[52] Wang C, Zhang P, Chen X, Yu J and Zhai H 2017 Phys. Rev. Lett 118 185701
[53] Yu J 2017 Phys. Rev. A 96 023601
[54] Caio M D, Cooper N R and Bhaseen M J 2015 Phys. Rev. Lett 115 236403
[55] Mardanya S, Bhattacharya U, Agarwal A and Dutta A 2018 Phys. Rev. B 97 115443
[56] Liou S F and Yang K 2018 Phys. Rev. B 97 235144
[57] Ji H X, Mo L H and Wan X 2022 Chin. Phys. Lett. 39 030301
[58] Mo L H, Zhang Q L and Wan X 2020 Chin. Phys. Lett. 37 060301
[59] Sambe H 1973 Phys. Rev. A 7 2203
[60] Chen C, An J H and Luo H G 2015 Phys. Rev. A 91 052122
[61] Mitra S, Jiménez-Gal án Á, Aulich M, Neuhaus M, Silva R E F, Pervak V, Kling M F and Biswas S 2024 Nature 62 752
[62] Zhao W, Kang K, Zhang Y, Knüppel P, Tao Z, Li L, Tschirhart C L, Redekop E, Watanabe K, Taniguchi T, Young A F, Shan J and Mak K F 2024 Nat. Phys. 20 275
[63] Tarnowski M, Ünal F N, Fläschner N, Rem B S, Eckardt A, Sengstock K and Weitenberg C 2019 Nat. Commun. 10 1728
[64] Fläschner N and Vogel D, Tarnowski M, Rem B S, L ühmann D-S, Heyl M, Budich J C, Mathey L, Sengstock K and Weitenberg C 2018 Nat. Phys. 14 265
[65] Miao J, Liu B and Zheng W 2015 Phys. Rev. B 91 033404
[66] Keleş A, Zhao E and Liu W V 2017 Phys. Rev. A 95 063619
[67] Chen H and Liu W V 2021 Phys. Rev. A 104 013308
[68] Das D, Ghosh R and Sengupta K 2021 J. High Energ. Phys. 2021 1-39
[69] Perez-Piskunow P M, Usaj G, Balseiro C A and Foa Torres L E F 2014 Phys. Rev. B 89 121401

[1]	Dynamical localization in a non-Hermitian Floquet synthetic system Han Ke(可汗), Jiaming Zhang(张嘉明), Liang Huo(霍良), and Wen-Lei Zhao(赵文垒). Chin. Phys. B, 2024, 33(5): 050507.

[1]	DENG WEN-JI (邓文基), LIU YOU-YAN (刘有延), HUANG XIU-QING (黄秀清). ON THE LOCALIZATION OF ELECTRONIC STATES IN ONE-DIMENSIONAL QUASILATTICES[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 113 -122 .
[2]	WANG JIAN (王坚), WU XING-FANG (吴杏芳), FANG ZHENG-ZHI (方正知). DIFFUSIVE AGGREGATION ON ION IMPLANTED THIN FILMS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(2): 81 -85 .
[3]	LIANG CAN-BIN (梁灿彬), SHANG YU-MING (商聿明). PLANE SYMMETRIC GENERAL SOLUTION TO EINSTEIN-MAXWELL EQUATIONS IN HIGHER DIMENSIONS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(3): 161 -166 .
[4]	PENG WEN-JI (彭文基), LI QING-XING (李庆行), YU ZHEN-XIN (余振新), AN NING (安宁), XU MAI (徐迈). STUDIES ON THE DYNAMICS OF OPTICAL BISTABILITY SWITCHING IN THE INTERNAL FABRY-PEROT CAVITY WITH A CdS_xSe_1-x-DOPED GLASS CHANNEL WAVEGUIDE[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(3): 183 -190 .
[5]	CHEN ANG (陈昂), ZHI YU (智宇), LI BIAO-RONG (李标荣), ZHANG XU-LI (张绪礼), TANG CHAO-QUN (唐超群), LI XIAO-HUA (李晓华), WANG SHAO-JIE (王少阶). POSITRON ANNIHILATION STUDY OF YBa₂(Cu_1-xSn_x)₃O_y SUPERCONDUCTORS[J]. Acta Physica Sinica (Overseas Edition), 1992, 1(3): 219 -223 .
[6]	PENG YU-FENG (彭玉峰), TANG JUN-XIONG (汤俊雄), WANG QING-JI (王庆吉). STUDY OF FARADAY ANOMALOUS DISPERSION SPECTRA OF THE HYPERFINE STRUCTURE OF Rb D₂ LINES[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(1): 1 -8 .
[7]	JIANG ZHAN-KUI (蒋占魁), PENG WEI-XIAN (彭慰先), GUO CHUAN (郭川), YU YING-NING (于英宁), YU HUA (于华). STUDIES ON HYPERFINE STRUCTURE AND ISOTOPE SHIFT OF SOME EXCITED STATES IN Yb AND Tm ATOMS[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(11): 801 -806 .
[8]	HE YU-LIANG (何宇亮), LIU XIANG-NA (刘湘娜), YIN CHENG-ZHONG (殷晨钟), ZHANG YU (张昱). DEPOSITION OF HIGH QUALITY AMORPHOUS SILICON FILMS WITH STRONG HYDROGEN DILUTED SILANE AS REACTANT GAS SOURCE[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(11): 807 -815 .
[9]	FENG YONG (冯勇), ZHOU LIAN (周廉), WANG KE-GUANG (王克光), DU MING-HUAN (杜明焕), ZHANG YU-HENG (张裕恒), LU YA-FENG (卢亚锋), JIN XIN (金新), ZHANG YI-TONG (张贻瞳), JIN JI-RONG (金继荣), YAO XI-XIAN (姚希贤). CRITICAL CURRENT DENSITY OF Y-Ba-Cu-Sn-O SUPERCONDUCTORS[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(11): 857 -862 .
[10]	ZHOU HAI-JUN (周海军), XU XIANG-YUAN (许祥源), HUANG WEN (黄雯), CHEN DIE-YAN (陈瓞延). NEW AUTOIONIZING STATES NEAR THE FIRST IONIZATION LIMIT OF RARE EARTH ELEMENT Dy[J]. Acta Physica Sinica (Overseas Edition), 1993, 2(12): 917 -924 .

Viewed

Full text

Abstract

Cited

Metrics
Related Articles

Phase diagram and quench dynamics of a periodically driven Haldane model

Cite this article:

Online attention