具有三体相互作用的自旋链系统中的几何相位与量子相变

单传家

doi:10.7498/aps.61.220302

摘要

本文首先对具有三体相互作用的一维自旋链系统的哈密顿量进行了对角化. 然后通过一个旋转操作求解了系统基态的几何相位, 通过数值计算几何相位及其导数随外界参数的变化, 考虑三体相互作用对几何相位以及量子相变的影响, 结果表明几何相位可以很好的用来表征该系统中的量子相变, 并且发现三体相互作用不但引起相变点平移, 而且可以产生新的临界点.

关键词:

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.

Keywords:

作者及机构信息

单传家

1.
湖北师范学院物理与电子科学学院, 黄石 435002

基金项目: 国家自然科学基金(批准号: 11105049), 湖北省自然科学基金(批准号: Q20112501, 2011CDC010) 和湖北师范学院青年项目(批准号: 2010C20)资助的课题.

Authors and contacts

Shan Chuan-Jia

1.
College of Physics and Electronic Science, Hubei Normal University, Huangshi 435002, China

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).

参考文献

[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

施引文献

[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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