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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 |
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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.
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Received: 29 October 2021
Revised: 19 December 2021
Accepted manuscript online: 12 January 2022
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PACS:
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05.30.-d
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(Quantum statistical mechanics)
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75.10.Pq
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(Spin chain models)
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05.30.Rt
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(Quantum phase transitions)
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| Fund: This work was supported by the National Natural Science Foundation of China (Grant Nos. 11975126 and 11575087). |
Corresponding Authors:
Peiqing Tong
E-mail: pqtong@njnu.edu.cn
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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
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[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 |
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