Please wait a minute...
Chin. Phys. B, 2022, Vol. 31(6): 060505    DOI: 10.1088/1674-1056/ac4a6e
GENERAL Prev   Next  

Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions

Kaiyuan Cao(曹凯源)1, Ming Zhong(钟鸣)1, and Peiqing Tong(童培庆)1,2,†
1 Department of Physics and Institute of Theoretical Physics, Nanjing Normal University, Nanjing 210023, China;
2 Jiangsu Key Laboratory for Numerical Simulation of Large Scale Complex Systems, Nanjing Normal University, Nanjing 210023, China
Abstract  We study the dynamical quantum phase transitions (DQPTs) in the $XY$ chains with the Dzyaloshinskii-Moriya interaction and the $XZY$-$YZX$ type of three-site interaction after a sudden quench. Both the models can be mapped to the spinless free fermion models by the Jordan-Wigner and Bogoliubov transformations with the form $H=\sum_{k}ǎrepsilon_{k}(\eta^{†}_{k}\eta_{k}-\frac{1}{2})$, where the quasiparticle excitation spectra $ǎrepsilon_{k}$ may be smaller than 0 for some $k$ and are asymmetrical ($ǎrepsilon_{k}\neqǎrepsilon_{-k}$). It is found that the factors of Loschmidt echo equal 1 for some $k$ corresponding to the quasiparticle excitation spectra of the pre-quench Hamiltonian satisfying $ǎrepsilon_{k}\cdotǎrepsilon_{-k}<0$, when the quench is from the gapless phase. By considering the quench from different ground states, we obtain the conditions for the occurrence of DQPTs for the general $XY$ chains with gapless phase, and find that the DQPTs may not occur in the quench across the quantum phase transitions regardless of whether the quench is from the gapless phase to gapped phase or from the gapped phase to gapless phase. This is different from the DQPTs in the case of quench from the gapped phase to gapped phase, in which the DQPTs will always appear. Moreover, we analyze the different reasons for the absence of DQPTs in the quench from the gapless phase and the gapped phase. The conclusion can also be extended to the general quantum spin chains.
Keywords:  dynamical quantum phase transition      gapless phase      asymmetry excitation spectra  
Received:  29 October 2021      Revised:  19 December 2021      Accepted manuscript online:  12 January 2022
PACS:  05.30.-d (Quantum statistical mechanics)  
  75.10.Pq (Spin chain models)  
  05.30.Rt (Quantum phase transitions)  
Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos. 11975126 and 11575087).
Corresponding Authors:  Peiqing Tong     E-mail:

Cite this article: 

Kaiyuan Cao(曹凯源), Ming Zhong(钟鸣), and Peiqing Tong(童培庆) Dynamical quantum phase transition in XY chains with the Dzyaloshinskii-Moriya and XZY-YZX three-site interactions 2022 Chin. Phys. B 31 060505

[1] Vojta T 2002 Quantum Phase Transitions in Computational Statistical Physics (Berlin: Springer) p. 211
[2] Sachdev S 2000 Quantum Phase Transitions (Cambridge: Cambridge University Press)
[3] Heyl M, Polkovnikov A and Kehrein S 2013 Phys. Rev. Lett. 110 135704
[4] Karrasch C and Schuricht D 2013 Phys. Rev. B 87 195104
[5] Hickey J M, Genway S and Garrahan J P 2017 Phys. Rev. B 89 054301
[6] Vajna S and Dora B 2014 Phys. Rev. B 89 161105
[7] Heyl M 2015 Phys. Rev. Lett. 115 140502
[8] Vajna S and Dora B 2015 Phys. Rev. B 91 155127
[9] Budich J C and Heyl M 2016 Phys. Rev. B 93 085416
[10] Huang Z and Balatsky A V 2016 Phys. Rev. Lett. 117 086416
[11] Zvyagin A A 2016 Low Temp. Phys. 42 971
[12] Halimeh J C and Valentin Z S 2017 Phys. Rev. B 96 134427
[13] Heyl M and Budich J C 2017 Phys. Rev. B 96 180304
[14] Homrighausen I, Abeling N O, Valentin Z and Halimeh J C 2017 Phys. Rev. B 96 104436
[15] Heyl M 2018 Rep. Prog. Phys. 81 054001
[16] Cheraghi H and Mahdavifar S 2018 J. Phys.: Conden. Matter 30 42LT01
[17] Wang P and Gao X 2018 Phys. Rev. A 97 023627
[18] Yin H, Chen S, Gao X and Wang P 2018 Phys. Rev. A 97 033624
[19] Zhou L, Wang Q, Wang H and Gong J 2018 Phys. Rev. A 98 022129
[20] Lang H, Chen Y, Hong Q and Fan H 2018 Phys. Rev. B 98 134310
[21] Huang Y P, Banerjee D and Heyl M 2019 Phys. Rev. Lett. 122 250401
[22] Jafari R 2019 Sci. Rep. 9 2871
[23] Liu T and Guo H 2019 Phys. Rev. B 99 104307
[24] Yang K, Zhou L, Ma W, Kong X, Wang P, Qin X, Rong X, Wang Y, Shi F, Gong J and Du J 2019 Phys. Rev. B 100 085308
[25] Chen S and Yang C 2019 Acta Phys. Sin. 68 220304 (in Chinese)
[26] Deng T and Yi W 2019 Acta Phys. Sin. 68 040303 (in Chinese)
[27] Haldar S, Roy S, Chanda T, Sen(De) A and Sen U 2020 Phys. Rev. B 101 224304
[28] Cao K, Li W, Zhong M and Tong P 2020 Phys. Rev. B 102 014207
[29] Hou X Y, Gao Q C, Guo H, He Y, Liu T and Chien C C 2020 Phys. Rev. B 102 104305
[30] Zamani S, Jafari R and Langari A 2020 Phys. Rev. B 102 144306
[31] Fu H, Cao K, Zhong M and Tong P 2021 Acta Phys. Sin. 70 480502 (in Chinese)
[32] Jurcevic P, Shen H, Hauke P, Maier C, Brydges T, Hempel C, Lanyon B P, Heyl M, Blatt R and Roos C F 2017 Phys. Rev. Lett. 119 080501
[33] Zhang J, Pagano G, Hess P W, Kyprianidis A, Becker P, Kaplan H, Gorshkov A V, Gong Z X and Monroe C 2017 Nature 551 601
[34] Wang K, Qiu X, Xiao L, Zhan X, Bian Z, Yi W and Xue P 2019 Phys. Rev. Lett. 122 020501
[35] Nie X, Wei B B, Chen X, Zhang Z, Zhao X, Qiu C, Tian Yu, Ji Y, Xin T, Lu D and Li J 2020 Phys. Rev. Lett. 124 250601
[36] Tian T, Yang H X, Qiu L Y, Liang H Y, Yang Y B, Xu Y and Duan L M 2020 Phys. Rev. Lett. 124 043001
[37] Xu X Y, Wang Q Q, Heyl M, Budich J C, Pan W W, Chen Z, Munsif J, Sun K, Xu J S, Han Y J, Li C F and Guo G C 2020 Light: Sci. Appl. 9 7
[38] Dzyaloshinsky I 1958 J. Phys. Chem. Solids 4 241
[39] Moriya T 1960 Phys. Rev. Lett. 4 228
[40] Derzhko O and Richter J 1999 Phys. Rev. B 59 100
[41] Yang J, Li J, Lin L and Zhu J J 2020 Chin. Phys. Lett. 37 087501
[42] Krokhmalskii T, Derzhko O, Stolze J and Verkholyak T 2008 Phys. Rev. B 77 174404
[43] Gottlieb D and Rossler J 1999 Phys. Rev. B 60 9232
[44] Kitaev A 2006 Ann. Phys. 321 2
[45] Rodney M, Song H F, Lee S S, Le H K and Srensen E S 2013 Phys. Rev. B 87 115132
[46] Suzuki S, Inoue J, and Chakrabarti B K 2013 Transverse Ising Chain (Pure System) in Quantum Ising Phases and Transitions in Transverse Ising Models (Berlin: Springer)) p. 13
[47] Zhong M, Xu H, Liu X X and Tong P 2013 Chin. Phys. B 22 090313
[48] Liu X, Zhong M, Xu H and Tong P 2012 J. Stat. Mech. 2012 P01003
[1] Variational quantum simulation of thermal statistical states on a superconducting quantum processer
Xue-Yi Guo(郭学仪), Shang-Shu Li(李尚书), Xiao Xiao(效骁), Zhong-Cheng Xiang(相忠诚), Zi-Yong Ge(葛自勇), He-Kang Li(李贺康), Peng-Tao Song(宋鹏涛), Yi Peng(彭益), Zhan Wang(王战), Kai Xu(许凯), Pan Zhang(张潘), Lei Wang(王磊), Dong-Ning Zheng(郑东宁), and Heng Fan(范桁). Chin. Phys. B, 2023, 32(1): 010307.
[2] Thermodynamic properties of two-dimensional charged spin-1/2 Fermi gases
Jia-Ying Yang(杨家营), Xu Liu(刘旭), Ji-Hong Qin(秦吉红), and Huai-Ming Guo(郭怀明). Chin. Phys. B, 2022, 31(6): 060504.
[3] Universal quantum circuit evaluation on encrypted data using probabilistic quantum homomorphic encryption scheme
Jing-Wen Zhang(张静文), Xiu-Bo Chen(陈秀波), Gang Xu(徐刚), and Yi-Xian Yang(杨义先). Chin. Phys. B, 2021, 30(7): 070309.
[4] Continuous-variable quantum key distribution based on photon addition operation
Xiao-Ting Chen(陈小婷), Lu-Ping Zhang(张露萍), Shou-Kang Chang(常守康), Huan Zhang(张欢), and Li-Yun Hu(胡利云). Chin. Phys. B, 2021, 30(6): 060304.
[5] Nonclassicality of photon-modulated atomic coherent states in the Schwinger bosonic realization
Jisuo Wang(王继锁), Xiangguo Meng(孟祥国), and Xiaoyan Zhang(张晓燕). Chin. Phys. B, 2020, 29(12): 124213.
[6] Generating two-dimensional quantum gases with high stability
Bo Xiao(肖波), Xuan-Kai Wang(王宣恺), Yong-Guang Zheng(郑永光), Yu-Meng Yang(杨雨萌), Wei-Yong Zhang(章维勇), Guo-Xian Su(苏国贤), Meng-Da Li(李梦达), Xiao Jiang(江晓), Zhen-Sheng Yuan(苑震生). Chin. Phys. B, 2020, 29(7): 076701.
[7] Effect of system-reservoir correlations on temperature estimation
Wen-Li Zhu(朱雯丽), Wei Wu(吴威), Hong-Gang Luo(罗洪刚). Chin. Phys. B, 2020, 29(2): 020501.
[8] Finite-dimensional pair coherent state engendered via the nonlinear Bose operator realization and its Wigner phase-space distributions
Jianming Liu(刘建明), Xiangguo Meng(孟祥国). Chin. Phys. B, 2019, 28(12): 124206.
[9] Atom-pair tunneling and quantum phase transition in asymmetry double-well trap in strong-interaction regime
Ji-Li Liu(刘吉利), Jiu-Qing Liang(梁九卿). Chin. Phys. B, 2019, 28(11): 110304.
[10] Dynamical evolution of photon-added thermal state in thermal reservoir
Xue-Xiang Xu(徐学翔), Hong-Chun Yuan(袁洪春). Chin. Phys. B, 2019, 28(11): 110301.
[11] Steady-state entanglement and heat current of two coupled qubits in two baths without rotating wave approximation
Mei-Jiao Wang(王美姣), Yun-Jie Xia(夏云杰). Chin. Phys. B, 2019, 28(6): 060303.
[12] Generalized Lanczos method for systematic optimization of tensor network states
Rui-Zhen Huang(黄瑞珍), Hai-Jun Liao(廖海军), Zhi-Yuan Liu(刘志远), Hai-Dong Xie(谢海东), Zhi-Yuan Xie(谢志远), Hui-Hai Zhao(赵汇海), Jing Chen(陈靖), Tao Xiang(向涛). Chin. Phys. B, 2018, 27(7): 070501.
[13] Identifying the closeness of eigenstates in quantum many-body systems
Hai-bin Li(李海彬), Yang Yang(杨扬), Pei Wang(王沛), Xiao-guang Wang(王晓光). Chin. Phys. B, 2017, 26(8): 080502.
[14] Enhanced electron-positron pair production by frequency chirping in one- and two-color laser pulse fields
Nuriman Abdukerim, Zi-Liang Li(李子良), Bai-Song Xie(谢柏松). Chin. Phys. B, 2017, 26(2): 020301.
[15] Thermal vacuum state corresponding to squeezed chaotic light and its application
Wan Zhi-Long (万志龙), Fan Hong-Yi (范洪义), Wang Zhen (王震). Chin. Phys. B, 2015, 24(12): 120301.
No Suggested Reading articles found!