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一维扩展量子罗盘模型的拓扑序和量子相变

陈西浩 王秀娟

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一维扩展量子罗盘模型的拓扑序和量子相变

陈西浩, 王秀娟

Topological orders and quantum phase transitions in a one-dimensional extended quantum compass model

Chen Xi-Hao, Wang Xiu-Juan
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  • 应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.
    By using the infinite time evolving block decimation in the presentation of infinite matrix product states, we study an extended quantum compass model (EQCM). This model does not only include extremely rich phase diagrams due to competitions of orbital degrees of freedom and anisotropic couplings between pseudospin-1/2 operators but also have the capacity to describe property of protected qubits for quantum computation which leads to lots of attentions paid to the phase boundaries of the EQCM. However, few attentions are paid to long-range topological string correlation order parameters of the EQCM. To study order parameters, one should understand spontaneous symmetry breaking which relates to Landau quantum phase transitions theory. Once spontaneous symmetry breaking happens, there should exist some local order which can be described by a local order parameter. This order parameter can be used to distinguish the phase from others. For continuous quantum phase transitions, in the critical regime, critical exponents can be extracted. Unfortunately, the long-range topological string correlation orders are beyond Landau quantum phase transitions theory, one can not directly use two paradigms of Landau-Ginzburg-Wilson. Usually, one can define a local order parameter by local magnetization. Naturally, one can also refer to this way to define the long-range topological string correlation order parameters by long-range topological string correlations on the following conditions, i.e. the quantum system undergoes a hidden spontaneous symmetry breaking; the long-range topological string correlation order parameter can be used to distinguish the phase from others; for continuous quantum phase transitions, the long-range topological string correlation order parameter satisfies scaling law when control parameter getting close to critical point. Based on above idea, in order to characterize the topological ordered phases and quantum phase transitions in the EQCM, even/odd long-range topological string correlations are introduced based on even/odd bonds. Hereafter, fidelity per lattice site, even/odd long-range topological string correlations, the saturation behavior of odd long-range topological string correlations and order parameters are calculated. The long-range topological string correlations show three distinguished behaviors which include decaying to zero, monotonic saturation and oscillatory saturation. By the above characterizations, oscillatory/monotonic odd long-range topological string correlation order parameter is derived. Then ground-state phase diagram of order parameters is computed which includes oscillatory/monotonic odd long-range topological string correlation order phase and antiferromagnetic phase. In the critical regime, critical exponent β=1/8 extracted from monotonic odd long-range topological string correlation order parameter and local magnetization shows the phase transition belongs to Ising universality. In addition, the phase transition points, the order of the phase transitions of fidelity show consistent with the results of order parameters.
      通信作者: 王秀娟, shanshui510@163.com
      Corresponding author: Wang Xiu-Juan, shanshui510@163.com
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    Liu G H, Li W, You W L, Tian G S, Su G 2012 Phys. Rev. B 85 184422

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    Wang L C, Yi X X 2010 Eur. Phys. J. D 77 281

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    Jafari R 2011 Phys. Rev. B 84 035112

    [14]

    Motamedifar M, Mahdavifar S, Shayesteh S F 2011 Eur. Phys. J. B 83 181

    [15]

    You W L 2012 Eur. Phys. J. B 85 83

    [16]

    Liu G H, Li W, You W L 2012 Eur. Phys. J. B 85 168

    [17]

    Vidal G 2007 Phys. Rev. Lett. 98 070201

    [18]

    Zhou H Q 2008 arXiv:0803.0585v1 [cond-mat.stat-mech]

    [19]

    Wang H T, Cho S Y, Batchelor M T 2015 arXiv:1508.01316 [quant-ph]

    [20]

    Zhou H, Barjaktarevi J P 2008 J. Phys. A:Math. Theor. 41 412001

    [21]

    Su Y H, Chen A M, Wang H L, Xiang C H 2017 Acta Phys. Sin. 66 120301 (in Chinese) [苏耀恒, 陈爱民, 王洪雷, 相春环 2017 物理学报 66 120301]

    [22]

    Kennedy T, Tasaki H 1992 Phys. Rev. B 45 304

    [23]

    Hida K 1992 Phys. Rev. B 45 2207

    [24]

    Chen X H, Cho S Y, Zhou H Q 2016 J. Korean Phys. Soc. 68 1114

    [25]

    Wang H T, Li B, Cho S Y 2013 Phys. Rev. B 87 054402

    [26]

    Hatsugai Y 2007 J. Phys.:Condens. Matter 19 145209

    [27]

    Pollmann F, Berg E, Turner A, Oshikawa M 2012 Phys. Rev. B 85 075125

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    Su Y H, Cho S Y, Li B, Wang H L, Zhou H Q 2012 J. Phys. Soc. Jpn. 81 074003

  • [1]

    Kugel K I, Khomskii D I 1973 Zh. Eksp. Teor. Fiz. 64 1429

    [2]

    Doucot B, Feigelán M V, IoffeL B, Ioselevich A S 2005 Phys. Rev. B 71 024505

    [3]

    Milman P, Maineult W, Guibal S, Guidoni L, Douot B, Ioffe L, Coudreau T 2007 Phys. Rev. Lett. 99 020503

    [4]

    Brzezicki W, Dziarmaga J, Olés A M 2007 Phys. Rev. B 75 134418

    [5]

    You W L, Tian G S 2008 Phys. Rev. B 78 184406

    [6]

    Brzezicki W, Olés A M 2009 Acta Phys. Pol. A 115 162

    [7]

    Sun K W, Zhang Y Y, Chen Q H 2009 Phys. Rev. B 79 104429

    [8]

    Sun K W, Chen Q H 2009 Phys. Rev. B 80 174417

    [9]

    Wang H T, Cho S Y 2015 J. Phys.:Condens. Matter 27 015603

    [10]

    Eriksson E, Johannesson H 2009 Phys. Rev. B 79 224424

    [11]

    Liu G H, Li W, You W L, Tian G S, Su G 2012 Phys. Rev. B 85 184422

    [12]

    Wang L C, Yi X X 2010 Eur. Phys. J. D 77 281

    [13]

    Jafari R 2011 Phys. Rev. B 84 035112

    [14]

    Motamedifar M, Mahdavifar S, Shayesteh S F 2011 Eur. Phys. J. B 83 181

    [15]

    You W L 2012 Eur. Phys. J. B 85 83

    [16]

    Liu G H, Li W, You W L 2012 Eur. Phys. J. B 85 168

    [17]

    Vidal G 2007 Phys. Rev. Lett. 98 070201

    [18]

    Zhou H Q 2008 arXiv:0803.0585v1 [cond-mat.stat-mech]

    [19]

    Wang H T, Cho S Y, Batchelor M T 2015 arXiv:1508.01316 [quant-ph]

    [20]

    Zhou H, Barjaktarevi J P 2008 J. Phys. A:Math. Theor. 41 412001

    [21]

    Su Y H, Chen A M, Wang H L, Xiang C H 2017 Acta Phys. Sin. 66 120301 (in Chinese) [苏耀恒, 陈爱民, 王洪雷, 相春环 2017 物理学报 66 120301]

    [22]

    Kennedy T, Tasaki H 1992 Phys. Rev. B 45 304

    [23]

    Hida K 1992 Phys. Rev. B 45 2207

    [24]

    Chen X H, Cho S Y, Zhou H Q 2016 J. Korean Phys. Soc. 68 1114

    [25]

    Wang H T, Li B, Cho S Y 2013 Phys. Rev. B 87 054402

    [26]

    Hatsugai Y 2007 J. Phys.:Condens. Matter 19 145209

    [27]

    Pollmann F, Berg E, Turner A, Oshikawa M 2012 Phys. Rev. B 85 075125

    [28]

    Su Y H, Cho S Y, Li B, Wang H L, Zhou H Q 2012 J. Phys. Soc. Jpn. 81 074003

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出版历程
  • 收稿日期:  2018-04-30
  • 修回日期:  2018-07-13
  • 刊出日期:  2018-10-05

一维扩展量子罗盘模型的拓扑序和量子相变

  • 1. 重庆大学材料科学与工程博士后流动站, 重庆 400030;
  • 2. 重庆大学, 输配电装备及系统安全与新技术国家重点实验室, 重庆 400044;
  • 3. 重庆大学物理学院, 重庆 400044
  • 通信作者: 王秀娟, shanshui510@163.com

摘要: 应用矩阵乘积态表示的无限虚时间演化块算法,研究了扩展的量子罗盘模型.为了深入研究该模型的长程拓扑序和量子相变,基于奇数键和偶数键,引入了奇数弦关联和偶数弦关联,计算了保真度、奇数弦关联、偶数弦关联、奇数弦关联饱和性与序参量.弦关联表现出三种截然不同的行为:衰减为零、单调饱和与振荡饱和.基于弦关联的以上特征,给出了量子罗盘模型的基态序参量相图.在临界区,局域磁化强度和单调奇弦序参量的临界指数β=1/8表明:相变的普适类是Ising类型.此外,保真度探测到的相变点、连续性与非连续性和序参量的结果一致.

English Abstract

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