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Berry phase and quantum phase transition in spin chain system with three-site interaction

Shan Chuan-Jia

Berry phase and quantum phase transition in spin chain system with three-site interaction

Shan Chuan-Jia
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  • In this paper, we diagonalize the Hamiltonian of the one-dimensional spin chain system with three-body interaction. Then we solve geometric phase of ground state in the system through a rotating operation. By the numerical calculation of the geometric phase and its derivative, we consider the three-body interaction effects on the geometric phase and quantum phase transition, the results show that the geometric phase can be well used to characterize quantum phase transition in this system, and find that three-body interaction not only can move the criticality region, but also can generate a new critical point.
    • Funds: Project supported by the National Natural Science Foundation of China(Grant No 11105049), the Natural Science Foundation of Hubei Province (Grant Nos. Q20112501, 2011CDC010), and the Programme of Hubei Normal University (Grant No. 2010C20).
    [1]

    Sachdev S 1999 Quantum Phase Transitions (Cambridge University Press, Cambridge, England)

    [2]

    Osterloh A, Amico L, Falci G 2002 Nature 416 608

    [3]

    Wu L A, Sarandy M S, Lidar D A 2004 Phys. Rev. Lett. 93 250404

    [4]

    Yi X X, Cui H T, Wang L C 2006 Phys. Rev. A 74 054102

    [5]

    Gu S J, Lin H Q, Li Y Q 2003 Phys. Rev. A 68 042330

    [6]

    Shan C J, Liu J B, Cheng W W 2009 Chin. Phys. B 18 3687

    [7]

    You W L, Li Y, Gu S J 2007 Phys. Rev. E 76 022101

    [8]

    Chen S, Wang L, Gu S J, Wang Y P 2007 Phys. Rev. E 76 061108

    [9]

    Zanardi P, Quan H T, Wang X G, Sun C P 2007 Phys. Rev. A 75 032109

    [10]

    Quan H T, Song Z, Liu X F, Zanardi P, Sun C P 2006 Phys. Rev. Lett 96 140604

    [11]

    Cheng W W, Liu J M 2010 Phys. Rev. A 82 012308

    [12]

    Zhu X, Tong P Q 2008 Chin. Phys. B 17 1623

    [13]

    Wang L C, Shen J, Yi X X 2011 Chin. Phys. B 20 50306

    [14]

    Berry M V 1984 Proc. R. Soc. London, Ser. A 392 45

    [15]

    Carollo A C M, Pachos J K 2005 Phys. Rev. Lett. 95 157203

    [16]

    Zhu S L 2006 Phys. Rev. Lett. 96 077206

    [17]

    Zhu S L 2008 International Journal of Modern Physics B 22 561

    [18]

    Hamma A 2006 quant-ph /0602091

    [19]

    Peng X, Wu S, Li J 2010 Phys. Rev. Lett. 105 240405

    [20]

    Ma Y Q, Chen S 2009 Phys. Rev. A 79 022116

    [21]

    Cheng W W, Shan C J 2010 Physica B 405 4821

    [22]

    Wang L C, Yan J Y, Yi X X 2010 Chin. Phys. B 19 040512

    [23]

    Yin S, Tong D M 2009 Phys. Rev. A 79 044303

    [24]

    Yi X X, Tong D M, Wang L C 2006 Phys. Rev. A 73 052103

  • [1]

    Sachdev S 1999 Quantum Phase Transitions (Cambridge University Press, Cambridge, England)

    [2]

    Osterloh A, Amico L, Falci G 2002 Nature 416 608

    [3]

    Wu L A, Sarandy M S, Lidar D A 2004 Phys. Rev. Lett. 93 250404

    [4]

    Yi X X, Cui H T, Wang L C 2006 Phys. Rev. A 74 054102

    [5]

    Gu S J, Lin H Q, Li Y Q 2003 Phys. Rev. A 68 042330

    [6]

    Shan C J, Liu J B, Cheng W W 2009 Chin. Phys. B 18 3687

    [7]

    You W L, Li Y, Gu S J 2007 Phys. Rev. E 76 022101

    [8]

    Chen S, Wang L, Gu S J, Wang Y P 2007 Phys. Rev. E 76 061108

    [9]

    Zanardi P, Quan H T, Wang X G, Sun C P 2007 Phys. Rev. A 75 032109

    [10]

    Quan H T, Song Z, Liu X F, Zanardi P, Sun C P 2006 Phys. Rev. Lett 96 140604

    [11]

    Cheng W W, Liu J M 2010 Phys. Rev. A 82 012308

    [12]

    Zhu X, Tong P Q 2008 Chin. Phys. B 17 1623

    [13]

    Wang L C, Shen J, Yi X X 2011 Chin. Phys. B 20 50306

    [14]

    Berry M V 1984 Proc. R. Soc. London, Ser. A 392 45

    [15]

    Carollo A C M, Pachos J K 2005 Phys. Rev. Lett. 95 157203

    [16]

    Zhu S L 2006 Phys. Rev. Lett. 96 077206

    [17]

    Zhu S L 2008 International Journal of Modern Physics B 22 561

    [18]

    Hamma A 2006 quant-ph /0602091

    [19]

    Peng X, Wu S, Li J 2010 Phys. Rev. Lett. 105 240405

    [20]

    Ma Y Q, Chen S 2009 Phys. Rev. A 79 022116

    [21]

    Cheng W W, Shan C J 2010 Physica B 405 4821

    [22]

    Wang L C, Yan J Y, Yi X X 2010 Chin. Phys. B 19 040512

    [23]

    Yin S, Tong D M 2009 Phys. Rev. A 79 044303

    [24]

    Yi X X, Tong D M, Wang L C 2006 Phys. Rev. A 73 052103

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    [8] Zheng Ying-Hong, Chen Tong, Wang Ping, Chang Zhe. Properties of geometric phase under Galilean transformation. Acta Physica Sinica, 2007, 56(11): 6199-6203. doi: 10.7498/aps.56.6199
    [9] Zhu Hong-Yi, Shen Jian-Qi. . Acta Physica Sinica, 2002, 51(7): 1448-1452. doi: 10.7498/aps.51.1448
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  • Received Date:  09 April 2012
  • Accepted Date:  12 June 2012
  • Published Online:  20 November 2012

Berry phase and quantum phase transition in spin chain system with three-site interaction

  • 1. College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China
Fund Project:  Project supported by the National Natural Science Foundation of China(Grant No 11105049), the Natural Science Foundation of Hubei Province (Grant Nos. Q20112501, 2011CDC010), and the Programme of Hubei Normal University (Grant No. 2010C20).

Abstract: In this paper, we diagonalize the Hamiltonian of the one-dimensional spin chain system with three-body interaction. Then we solve geometric phase of ground state in the system through a rotating operation. By the numerical calculation of the geometric phase and its derivative, we consider the three-body interaction effects on the geometric phase and quantum phase transition, the results show that the geometric phase can be well used to characterize quantum phase transition in this system, and find that three-body interaction not only can move the criticality region, but also can generate a new critical point.

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