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首页> 外文期刊>Physical review >Transition from the Z_2 spin liquid to antiferromagnetic order: Spectrum on the torus
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Transition from the Z_2 spin liquid to antiferromagnetic order: Spectrum on the torus

机译：从Z_2自旋液体到反铁磁顺序的过渡：圆环上的光谱

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摘要

We describe the finite-size spectrum in the vicinity of the quantum critical point between a Z_2 spin liquid and a coplanar antiferromagnet on the torus. We obtain the universal evolution of all low-lying states in an antiferromagnet with global SU(2) spin rotation symmetry, as it moves from the fourfold topological degeneracy in a gapped Z_2 spin liquid to the Anderson "tower-of-states" in the ordered antiferromagnet. Due to the existence of nontrivial order on either side of this transition, this critical point cannot be described in a conventional Landau-Ginzburg-Wilson framework. Instead, it is described by a theory involving fractionalized degrees of freedom known as the O(4)~* model, whose spectrum is altered in a significant way by its proximity to a topologically ordered phase. We compute the spectrum by relating it to the spectrum of the O(4) Wilson-Fisher fixed point on the torus, modified with a selection rule on the states, and with nontrivial boundary conditions corresponding to topological sectors in the spin liquid. The spectrum of the critical 0(2N) model is calculated directly at N = 00, which then allows a reconstruction of the full spectrum of the O(2N)~* model at leading order in 1/N. This spectrum is a unique characteristic of the vicinity of a fractionalized quantum critical point, as well as a universal signature of the existence of proximate Z_2 topological and antiferromagnetically ordered phases, and can be compared with numerical computations on quantum antiferromagnets on two-dimensional lattices.
机译：我们描述了Z_2自旋液体和圆环上共面反铁磁体之间的量子临界点附近的有限尺寸谱。我们获得了具有全局SU（2）自旋旋转对称性的反铁磁体中所有低洼状态的普遍演化，因为它从空位Z_2自旋液体中的四重拓扑简并移到了安德森“状态塔”中。订购反铁磁体。由于此过渡过程的任一侧都存在非平凡的秩序，因此无法在传统的Landau-Ginzburg-Wilson框架中描述此临界点。取而代之的是用涉及分数自由度的理论（称为O（4）〜*模型）进行描述，该理论的光谱因其接近拓扑有序相而以显着方式改变。我们通过将光谱与圆环上O（4）Wilson-Fisher不动点的光谱相关联来计算光谱，并用状态选择规则进行修改，并使用与旋转液体中拓扑扇区相对应的非平凡边界条件。临界0（2N）模型的光谱直接在N = 00处计算，然后可以以1 / N的前导顺序重建O（2N）〜*模型的全光谱。该光谱是分数量子临界点附近的独特特征，也是附近Z_2拓扑和反铁磁有序相的存在的普遍特征，可以与二维晶格上的量子反铁磁体的数值计算进行比较。

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  • 来源
    《Physical review》 |2016年第8期|085134.1-085134.16|共16页
  • 作者

    Seth Whitsitt; Subir Sachdev;

  • 作者单位

    Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA;

    Department of Physics, Harvard University, Cambridge, Massachusetts, 02138, USA,Perimeter Institute for Theoretical Physics, Waterloo, Ontario N2L 2Y5, Canada;

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