Detection of symmetry-protected topological phases in one dimension
Detection of symmetry-protected topological phases in one dimension
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DOI：
10.1103/physrevb.86.125441
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发表时间：
2012-04
影响因子：
3.7
通讯作者：
F. Pollmann;A. Turner
中科院分区：
文献类型：
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作者：
F. Pollmann;A. Turner
拓扑相是一种不能用局部序参量来表征的物质相。研究表明，一维系统中的间隙对称相可以使用与对称群的射影表示相关的工具来完全表征。我们解释了在一维中检测这些对称保护拓扑相的两种方法。首先，我们给出了一种直接从矩阵-乘积状态表示中提取投影表示的数值方法。其次，我们导出了时间反转和反演对称的非局部序参数，并讨论了正则字符串序参数不能应用的局部对称的广义字符串序。进一步指出，这些拓扑相的非局部序参量实际上与拓扑表面有关。
A topological phase is a phase of matter which cannot be characterized by a local order parameter. It has been shown that gapped symmetric phases in one-dimensional (1D) systems can be completely characterized using tools related to projective representations of the symmetry groups. We explain two ways to detect these symmetry protected topological phases in 1D. First, we give a numerical approach for directly extracting the projective representations from a matrix-product state representation. Second, we derive nonlocal order parameters for time-reversal and inversion symmetry, and discuss a generalized string order for local symmetries for which the regular string-order parameter cannot be applied. We furthermore point out that the nonlocal order parameter for these topological phases is actually related to topological surfaces.