搜索

x

留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

具有次近邻相互作用的五量子比特XXZ海森伯自旋链的热纠缠

刘贵艳 毛竹 周斌

引用本文:
Citation:

具有次近邻相互作用的五量子比特XXZ海森伯自旋链的热纠缠

刘贵艳, 毛竹, 周斌

Thermal entanglement in a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction

Liu Gui-Yan, Mao Zhu, Zhou Bin
PDF
导出引用
  • 研究具有次近邻相互作用五量子比特XXZ海森伯自旋链在磁场作用下的热纠缠性质,利用数值计算求出最近邻两量子比特和次近邻两量子比特的共生纠缠度(concurrence),分别记为C12和C13.研究结果表明,阻挫参数对配对热纠缠具有重要影响,而且阻挫参数的变化对C12和C13的影响也各不相同;温度、磁场、Dzyaloshinkii-Moriya相互作用以及各向异性参数对配对热纠缠有着不同程度的影响;通过选择适当的模型参数,可以有效地调节和提高五量子比特XXZ海森伯自旋链的配对热纠缠.
    In the study of thermal entanglement of the Heisenberg spin chain model, one usually considers only the spin interaction between the nearest neighboring qubits. Actually, a generalized Heisenberg model, so-called J1-J2 Heisenberg model, which is constructed by considering the fact that not only the nearest neighboring but also the next nearest neighboring spin interaction also plays an important role. In J1-J2 Heisenberg model, due to the next nearest neighboring spin interaction, the frustration effect can occur and has an important influence on the magnetic properties of the model. In this paper we investigate the thermal entanglement of a five-qubit XXZ Heisenberg spin chain with the next nearest neighboring interaction in a magnetic field. Using the numerical method, we calculate the pairwise concurrences of the nearest neighbouring qubits and the next nearest neighboring qubits, abbreviated as C12 and C13 respectively. The numerical results show that the frustration parameter α has an important effect on the pairwise thermal entanglement. Moreover, C12 and C13 have different variations with the change of the frustration parameter α. Meanwhile, it is found that the temperature, magnetic field, Dzyaloshinkii-Moriya (DM) interaction and anisotropic parameter also have great effects on the thermal entanglement. The increasing of temperature can reduce the thermal entanglement. The magnetic field can enhance the thermal entanglement between both two nearest and next nearest neighboring qubits, but when the magnetic field becomes strong enough, only the thermal entanglement between the two nearest neighboring qubits is suppressed. A certain extent of DM interaction can enhance the thermal entanglement between the two nearest neighboring qubits. But for the next nearest neighboring qubits, without the magnetic field, the increasing of DM interaction mainly enlarge the entanglement vanishing area of frustration parameter α. When the system changes from anisotropic to isotropic state, the entanglement vanishing area also changes obviously for C12 and C13. Thus, we can choose appropriate magnetic field strength, temperature, frustration parameter, DM interaction parameter and anisotropic parameter to effectively control and enhance the thermal entanglement of the system.
      通信作者: 毛竹, maozhu@hubu.edu.cn;binzhou@hubu.edu.cn ; 周斌, maozhu@hubu.edu.cn;binzhou@hubu.edu.cn
    • 基金项目: 国家自然科学基金(批准号:11274102)、教育部新世纪优秀人才支持计划(批准号:NCET-11-0960)和博士点基金(博导类)(批准号:20134208110001)资助的课题.
      Corresponding author: Mao Zhu, maozhu@hubu.edu.cn;binzhou@hubu.edu.cn ; Zhou Bin, maozhu@hubu.edu.cn;binzhou@hubu.edu.cn
    • Funds: Project supported by the National Natural Science Foundation of China (Grant No. 11274102), the Program for New Century Excellent Talents in University of Ministry of Education of China (Grant No. NCET-11-0960), and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20134208110001).
    [1]

    Bennett C H, Brassard C, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895

    [2]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881

    [3]

    Ekert A K 1991 Phys. Rev. Lett. 67 661

    [4]

    Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901

    [5]

    Wang X G 2001 Phys. Rev. A 64 012313

    [6]

    Wang X G 2001 Phys. Lett. A 281 101

    [7]

    Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese)[张英丽, 周斌 2011 物理学报 60 120301]

    [8]

    Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311

    [9]

    Wang X G, Fu H C, Solomon A I 2001 J. Phys. A 34 11307

    [10]

    Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313

    [11]

    Wang Y H, Xia Y J 2009 Acta Phys. Sin. 58 7479 (in Chinese)[王彦辉, 夏云杰 2009 物理学报 58 7479]

    [12]

    Hu Z N, Yi K S, Park K S 2007 J. Phys. A: Math. Theor. 40 7283

    [13]

    Łuczak J, Bułka B R 2012 J. Phys.: Condens. Matter 24 375303

    [14]

    Zhou B 2011 Int. J. Mod. Phys. B 25 2135

    [15]

    Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1388

    [16]

    Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1399

    [17]

    Hase M, Terasaki I, Uchinokura K 1993 Phys. Rev. Lett. 70 3651

    [18]

    Bray J W, Interrante L V, Jacobs L S, Bonner J C 1983 Extended Linear Chain Compounds (Volume 3) (New York: Plenum Press) pp353-415

    [19]

    Gu S J, Li H, Li Y Q, Lin H Q 2004 Phys. Rev. A 70 052302

    [20]

    Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 358 363

    [21]

    Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 349 37

    [22]

    Chhajlany R W, Tomczak P, Wójcik A, Richter J 2007 Phys. Rev. A 75 032340

    [23]

    Liu R, Liang M L, Yuan B 2007 Eur. Phys. J. D 41 571

    [24]

    Eryiǧit R 2009 Int. J. Theor. Phys. 48 885

    [25]

    Kwek L C, Takahashi Y, Choo K W 2009 J. Phys.: Conf. Ser. 143 012014

    [26]

    Şahintaş A, Akyz C 2016 Physica A 448 10

    [27]

    Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022

    [28]

    Wootters W K 1998 Phys. Rev. Lett. 80 2245

    [29]

    Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306

  • [1]

    Bennett C H, Brassard C, Crépeau C, Jozsa R, Peres A, Wootters W K 1993 Phys. Rev. Lett. 70 1895

    [2]

    Bennett C H, Wiesner S J 1992 Phys. Rev. Lett. 69 2881

    [3]

    Ekert A K 1991 Phys. Rev. Lett. 67 661

    [4]

    Arnesen M C, Bose S, Vedral V 2001 Phys. Rev. Lett. 87 017901

    [5]

    Wang X G 2001 Phys. Rev. A 64 012313

    [6]

    Wang X G 2001 Phys. Lett. A 281 101

    [7]

    Zhang Y L, Zhou B 2011 Acta Phys. Sin. 60 120301 (in Chinese)[张英丽, 周斌 2011 物理学报 60 120301]

    [8]

    Cao M, Zhu S Q 2005 Phys. Rev. A 71 034311

    [9]

    Wang X G, Fu H C, Solomon A I 2001 J. Phys. A 34 11307

    [10]

    Hou J M, Du L, Ding J Y, Zhang W X 2010 Chin. Phys. B 19 110313

    [11]

    Wang Y H, Xia Y J 2009 Acta Phys. Sin. 58 7479 (in Chinese)[王彦辉, 夏云杰 2009 物理学报 58 7479]

    [12]

    Hu Z N, Yi K S, Park K S 2007 J. Phys. A: Math. Theor. 40 7283

    [13]

    Łuczak J, Bułka B R 2012 J. Phys.: Condens. Matter 24 375303

    [14]

    Zhou B 2011 Int. J. Mod. Phys. B 25 2135

    [15]

    Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1388

    [16]

    Majumdar C K, Ghosh D K 1969 J. Math. Phys. 10 1399

    [17]

    Hase M, Terasaki I, Uchinokura K 1993 Phys. Rev. Lett. 70 3651

    [18]

    Bray J W, Interrante L V, Jacobs L S, Bonner J C 1983 Extended Linear Chain Compounds (Volume 3) (New York: Plenum Press) pp353-415

    [19]

    Gu S J, Li H, Li Y Q, Lin H Q 2004 Phys. Rev. A 70 052302

    [20]

    Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 358 363

    [21]

    Eryiǧit R, Gndç Y, Eryiǧit R 2006 Phys. Lett. A 349 37

    [22]

    Chhajlany R W, Tomczak P, Wójcik A, Richter J 2007 Phys. Rev. A 75 032340

    [23]

    Liu R, Liang M L, Yuan B 2007 Eur. Phys. J. D 41 571

    [24]

    Eryiǧit R 2009 Int. J. Theor. Phys. 48 885

    [25]

    Kwek L C, Takahashi Y, Choo K W 2009 J. Phys.: Conf. Ser. 143 012014

    [26]

    Şahintaş A, Akyz C 2016 Physica A 448 10

    [27]

    Hill S, Wootters W K 1997 Phys. Rev. Lett. 78 5022

    [28]

    Wootters W K 1998 Phys. Rev. Lett. 80 2245

    [29]

    Coffman V, Kundu J, Wootters W K 2000 Phys. Rev. A 61 052306

  • [1] 陈爱民, 刘东昌, 段佳, 王洪雷, 相春环, 苏耀恒. 含有Dzyaloshinskii-Moriya相互作用的自旋1键交替海森伯模型的量子相变和拓扑序标度. 物理学报, 2020, 69(9): 090302. doi: 10.7498/aps.69.20191773
    [2] 谢元栋. 各向异性海森伯自旋链中的超椭圆函数波解. 物理学报, 2018, 67(19): 197502. doi: 10.7498/aps.67.20181005
    [3] 任杰, 顾利萍, 尤文龙. 带有三体相互作用的S=1自旋链中的保真率和纠缠熵. 物理学报, 2018, 67(2): 020302. doi: 10.7498/aps.67.20172087
    [4] 郑一丹, 毛竹, 周斌. 具有三角自旋环的伊辛-海森伯链的热纠缠. 物理学报, 2017, 66(23): 230304. doi: 10.7498/aps.66.230304
    [5] 谢元栋. 各向异性海森伯自旋链中的高阶孤子. 物理学报, 2016, 65(20): 207501. doi: 10.7498/aps.65.207501
    [6] 丛美艳, 杨晶, 黄燕霞. 在不同初态下Dzyaloshinskii-Moriya相互作用及内禀退相干对海森伯系统的量子纠缠的影响. 物理学报, 2016, 65(17): 170301. doi: 10.7498/aps.65.170301
    [7] 郑一丹, 周斌. {Cu3}单分子磁体在热平衡和磁场作用下的三体纠缠. 物理学报, 2016, 65(12): 120301. doi: 10.7498/aps.65.120301
    [8] 蒋建军, 杨翠红, 刘拥军. 一种等效于反铁磁海森伯混合自旋链的铁磁-反铁磁交替自旋链. 物理学报, 2012, 61(6): 067502. doi: 10.7498/aps.61.067502
    [9] 姜春蕾, 刘晓娟, 刘明伟, 王艳辉, 彭朝晖. 内禀退相干下海森伯XY模型中的热纠缠性质及其相干调控. 物理学报, 2012, 61(17): 170302. doi: 10.7498/aps.61.170302
    [10] 周宗立, 章国顺, 娄平. 相互作用突然开启后的反铁磁海森伯模型. 物理学报, 2011, 60(3): 031101. doi: 10.7498/aps.60.031101
    [11] 刘圣鑫, 李莎莎, 孔祥木. Dzyaloshinskii-Moriya相互作用对量子XY链中热纠缠的影响. 物理学报, 2011, 60(3): 030303. doi: 10.7498/aps.60.030303
    [12] 张英丽, 周斌. 具有Dzyaloshinskii-Moriya相互作用的四量子比特海森堡XXZ模型中的热纠缠. 物理学报, 2011, 60(12): 120301. doi: 10.7498/aps.60.120301
    [13] 王彦辉, 夏云杰. 具有Dzyaloshinskii-Moriya相互作用的三量子比特海森伯模型中的对纠缠. 物理学报, 2009, 58(11): 7479-7485. doi: 10.7498/aps.58.7479
    [14] 秦 猛, 田东平, 陶应娟. 自旋为1的三粒子Heisenberg XXX链中杂质对热纠缠的影响. 物理学报, 2008, 57(9): 5395-5399. doi: 10.7498/aps.57.5395
    [15] 张 涛, 惠小强, 岳瑞宏. 三量子位Heisenberg XX 链中杂质对纠缠的影响. 物理学报, 2004, 53(8): 2755-2760. doi: 10.7498/aps.53.2755
    [16] 冯培成, 王登龙. 计及次近邻非谐相互作用下原子链中的非线性元激发. 物理学报, 2003, 52(6): 1332-1336. doi: 10.7498/aps.52.1332
    [17] 王登龙, 颜晓红, 唐 翌. 考虑次近邻相互作用下一维单原子链中的孤立波. 物理学报, 2000, 49(9): 1736-1740. doi: 10.7498/aps.49.1736
    [18] 张海燕, 许伯威. 用共形不变性和Lanczos方法研究具有次近邻相互作用的一维量子链. 物理学报, 1994, 43(6): 864-871. doi: 10.7498/aps.43.864
    [19] 余超凡, 周义昌. 带有次近邻相互作用的非谐性线性链中亚声速和超声速孤子. 物理学报, 1994, 43(10): 1677-1687. doi: 10.7498/aps.43.1677
    [20] 王养璞. Ising自旋S=1,具有次近邻相互作用的面心立方格子的反铁磁体在外场下的基态能量. 物理学报, 1983, 32(7): 875-887. doi: 10.7498/aps.32.875
计量
  • 文章访问数:  5109
  • PDF下载量:  193
  • 被引次数: 0
出版历程
  • 收稿日期:  2017-07-17
  • 修回日期:  2017-09-12
  • 刊出日期:  2019-01-20

/

返回文章
返回