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Hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points

机译：具有so（N）_1个临界点的完全可解决的spin-1 / 2链的层次结构

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摘要

We construct a hierarchy of exactly solvable spin-1/2 chains with so(N)_1 critical points. Our construction is based on the framework of condensate-induced transitions between topological phases. We employ this framework to construct a Hamiltonian term that couples N transverse field Ising chains such that the resulting theory is critical and described by the so(N)_1 conformal field theory. By employing spin duality transformations, we then cast these spin chains for arbitrary N into translationally invariant forms that all allow exact solution by the means of a Jordan-Wigner transformation. For odd N our models generalize the phase diagram of the transverse field Ising chain, the simplest model in our hierarchy. For even N the models can be viewed as longer ranger generalizations of the XY chain, the next model in the hierarchy. We also demonstrate that our method of constructing spin chains with given critical points goes beyond exactly solvable models. Applying the same strategy to the Blume-Capel model, a spin-1 generalization of the Ising chain in a generic magnetic field, we construct another critical spin-1 chain with the predicted conformal field theory (CFT) describing the criticality.
机译：我们构建了具有so（N）_1个临界点的完全可解决的spin-1 / 2链的层次结构。我们的构建基于拓扑阶段之间凝结水诱发的过渡的框架。我们采用此框架来构造耦合N个横向场Ising链的哈密顿量，以使所得理论至关重要，并由so（N）_1共形场理论进行描述。通过使用自旋对偶变换，我们然后将这些旋转链用于任意N转换为翻译不变形式，所有形式都可以通过Jordan-Wigner变换进行精确求解。对于奇数N，我们的模型可以概括横向场Ising链的相图，这是我们层次结构中最简单的模型。对于偶数N，这些模型也可以看作是XY链的更长范围的概括，是层次结构中的下一个模型。我们还证明了构造具有给定临界点的自旋链的方法超越了完全可求解的模型。将相同的策略应用于Blume-Capel模型（通用磁场中Ising链的spin-1泛化），我们使用描述临界性的预测共形场理论（CFT）构造了另一个临界spin-1链。

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  • 来源
    《Physical review》 |2014年第1期|014409.1-014409.21|共21页
  • 作者

    Ville Lahtinen; Teresia Mansson; Eddy Ardonne;

  • 作者单位

    Institute for Theoretical Physics, University of Amsterdam, Science Park 904,1090 GL Amsterdam, The Netherlands ,Institute-Lorentz for Theoretical Physics, Leiden University, PO Box 9506, NL-2300 RA Leiden, The Netherlands;

    Department of Theoretical Physics, School of Engineering Sciences, Royal Institute of Technology (KTH), Roslagstullsbacken 21, SE-106 91 Stockholm, Sweden;

    Department of Physics, Stockholm University, AlbaNova University Center, SE-106 91 Stockholm, Sweden;

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  • 正文语种 eng
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  • 关键词

    spin chain models; quantized spin models; conformal field theory, algebraic structures;

    机译：自旋链模型;量化自旋模型共形场论;代数结构;

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