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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.
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Keywords:
- berry phase /
- quantum phase transition /
- three-site interaction
[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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[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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