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Numerical detection of symmetry-enriched topological phases with space-group symmetry

机译:具有空间群对称性的富对称拓扑相的数值检测

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摘要

Topologically ordered phases of matter, in particular so-called symmetry-enriched topological phases, can exhibit quantum number fractionalization in the presence of global symmetry. In Z_2 topologically ordered states in two dimensions, fundamental translations T_x and T_y acting on anyons can either commute or anticommute. This property, crystal momentum fractionalization, can be seen in a periodicity of the excited-state spectrum in the Brillouin zone. We present a numerical method to detect the presence of this form of symmetry enrichment given a projected entangled pair state; we study the minima of the spectrum of correlation lengths of the transfer matrix for a cylinder. As a benchmark, we demonstrate our method using a modified toric code model with perturbation. An enhanced periodicity in momentum clearly reveals the nontrivial anticommutation relation {T_x,T_y} = 0 for the corresponding quasiparticles in the system.
机译:物质的拓扑有序相,特别是所谓的富含对称性的拓扑相,在存在全局对称性时可以表现出量子数分级化。在二维的Z_2拓扑有序状态中,作用于任意子的基本平移T_x和T_y可以上下班。在布里渊区的激发态光谱的周期性中可以看到这种性质,即晶体动量分级。我们给出了一种数值方法来检测给定投影纠缠对状态下这种形式的对称富集的存在。我们研究了圆柱体传递矩阵相关长度谱的最小值。作为基准,我们使用带有扰动的改进的复曲面代码模型演示了我们的方法。动量周期性的增强清楚地揭示了系统中相应准粒子的非平凡的反换向关系{T_x,T_y} = 0。

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  • 来源
    《Physical review》 |2015年第12期|121103.1-121103.5|共5页
  • 作者单位

    Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA,Department of Physics, California Institute of Technology, Pasadena, California 91125, USA;

    Institute for Quantum Information and Matter, California Institute of Technology, Pasadena, California 91125, USA,Department of Physics, California Institute of Technology, Pasadena, California 91125, USA;

    Department of Physics, 390 UCB, University of Colorado, Boulder, Colorado 80309, USA;

    Department of Physics, California Institute of Technology, Pasadena, California 91125, USA;

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  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

    fractional statistics systems (anyons, etc.); excited states: methodology; quantized spin models;

    机译:分数统计系统(任何时间等);激发态:方法论量化自旋模型;

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