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Chinese Physics C> 2012, Vol. 36> Issue(6) : 479-484  DOI: 10.1088/1674-1137/36/6/001

Critical behavior of the XY spin chain with three-site interaction studied in terms of the Loschmidt echo

  •  School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China

  • The effect of the three-site interaction (α) on the critical behaviors of the XY spin chain is studied in terms of the Loschmidt echo (LE). The critical lines can be shifted by α, and the anisotropy parameter of the XY chain has no effect on the critical lines. The scaling behaviors of the LE reveal that the dynamical behaviors of the LE are reliable for characterizing quantum phase transition (QPT).
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    [1] Sachdev S. Quantum Phase Transition. Cambridge: Cambridge University Press, 1999[2] JIN G J, FENG D. Progr. Phys., 2009, 29: 325[3] Giorgi G L, Paganelli S, Galve F. Phys. Rev. A, 2010, 81: 052118[4] CHEN B L, KOU S P, ZHANG Y B et al. Phys. Rev. A, 2010, 81: 053608[5] WU L A, Sarandy M S, Lidar D A. Phys. Rev. Lett., 2004, 93: 250404[6] Zanardi P, Paunkovic N. Phys. Rev. E, 2006, 74: 031123[7] CHEN S, WANG L, HAO Y J et al. Phys. Rev. A, 2008, 77: 032111[8] YOU W L, LI Y W, GU S J. Phys. Rev. E, 2007, 76: 022101[9] CHENG W W, LIU J M. Phys. Rev. A, 2010, 82: 012308[10] LI Y C LIN H Q Phys. Rev. A, 2011, 83: 052323[11] Carollo A C M, Pachos J K. Phys. Rev. Lett., 2005, 95: 157203[12] ZHU S L. Phys. Rev. Lett., 2006, 96: 077206[13] ZHU J M. Chin. Phys. C (HEP NP), 2011, 35: 144[14] AI Q, WANG Y D, LONG G L et al. Sci. China Ser. G, 2009, 52: 1898[15] QUAN H T, SONG Z, LIU X F et al. Phys. Rev. Lett., 2006, 96: 140604[16] HUANG J F, LI Y, LIAO J Q et al. Phys. Rev. A, 2009, 80: 063829[17] ZHENG Q, WANG W G, ZHANG X P et al. Phys. Lett. A, 2008, 372: 5139[18] ZHENG Q, WANG W G, QIN P Q et al. Phys. Rev. E, 2009, 80: 016214[19] YUAN Z G, ZHANG P, LI S S. Phys. Rev. A, 2007, 75: 012102[20] LAI C Y, HUNG J T, MOU C Y et al. Phys. Rev. B, 2008, 77: 205419[21] ZHANG J F, Cucchietti F M, Chandrashekar C M et al. Phys. Rev. A, 2009, 79: 012305[22] LI M, FEI S M, Li-Jost X Q. Chin. Sci. Bull., 2011, 56: 945[23] MA X S, REN M F, ZHAO G X et al. Sci. Chin. Phys. Mech. Astron., 2011, 54: 1833[24] GUO K T, LIANG M C, XU H Y et al. Sci. Chin. Phys. Mech. Astron., 2011, 54: 491[25] Thouless D J. Proc. Phys. Soc., 1965, 86: 893[26] Roger M, Hetherington J H, Delrieu J M. Rev. Mod. Phys., 1983, 55: 1[27] Zvyagin A A. Phys. Rev. B, 2009, 80: 014414[28] LIU W Z, ZHANG J F, DENG Z W et al. Sci. Chin. Ser. G, 2008, 51: 1089[29] LIU W Z, ZHANG J F, LONG G L. Chin. Sci. Bull., 2009, 54: 4262[30] LIAN H L, TIAN D P. Phys. Lett. A, 2011, 375: 3604[31] LI Y C, LIN H Q. Phys. Rev. A, 2007, 76: 0421188

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LIAN Han-Li. Critical behavior of the XY spin chain with three-site interaction studied in terms of the Loschmidt echo[J]. Chinese Physics C, 2012, 36(6): 479-484. doi: 10.1088/1674-1137/36/6/001
LIAN Han-Li. Critical behavior of the XY spin chain with three-site interaction studied in terms of the Loschmidt echo[J]. Chinese Physics C, 2012, 36(6): 479-484.  doi: 10.1088/1674-1137/36/6/001 shu
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Received: 2011-11-30
Revised: 2012-02-03
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Critical behavior of the XY spin chain with three-site interaction studied in terms of the Loschmidt echo

    Corresponding author: LIAN Han-Li,
  • School of Science, Xi'an University of Posts and Telecommunications, Xi'an 710121, China
  • Received Date: 2011-11-30
  • Accepted Date: 2012-02-03
  • Available Online: 2012-06-05

Abstract: The effect of the three-site interaction (α) on the critical behaviors of the XY spin chain is studied in terms of the Loschmidt echo (LE). The critical lines can be shifted by α, and the anisotropy parameter of the XY chain has no effect on the critical lines. The scaling behaviors of the LE reveal that the dynamical behaviors of the LE are reliable for characterizing quantum phase transition (QPT).

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