对称保护拓扑相的隐序和通量附着：类Laughlin方法
Hidden order and flux attachment in symmetry protected topological phases: a Laughlin-like approach
摘要：
物质的拓扑相与常规相的不同之处在于它们缺乏局部序参量。在量子霍尔效应中，隐藏的序参量仍然存在，并构成了著名的复合粒子方法的基础。在二维和三维对称性保护拓扑相（SPT）中是否存在相似的隐序是一个很大的问题。在这里，我们介绍了一种新的方法产生SPT基态，基于一个推广的劳克林波函数。这种方法给出了一个简单的和统一的图片的一些类的SPT在1D和2D，并揭示了他们隐藏的顺序和通量连接结构。对于1D的情况下，我们得到精确的波函数之间的关系，以这种方式和群上同调波函数，以及矩阵产品状态分类。对于二维伊辛SPT，强有力的分析和数值证据表明，得到的波函数确实描述了所需的SPT。然后，伊辛SPT出现作为一个国家与准长程序的复合自由度组成的伊辛对称性收费附加到伊辛对称通量。
英文摘要：
Topological phases of matter are distinct from conventional ones by their lack of a local order parameter. Still in the quantum Hall effect, hidden order parameters exist and constitute the basis for the celebrated composite-particle approach. Whether similar hidden orders exist in 2D and 3D symmetry protected topological phases (SPTs) is a largely open question. Here we introduce a new approach for generating SPT groundstates, based on a generalization of the Laughlin wavefunction. This approach gives a simple and unifying picture of some classes of SPTs in 1D and 2D, and reveals their hidden order and flux attachment structures. For the 1D case, we derive exact relations between the wavefunctions obtained in this manner and group cohomology wavefunctions, as well as matrix product state classification. For the 2D Ising SPT, strong analytical and numerical evidence is given to show that the wavefunction obtained indeed describes the desired SPT. The Ising SPT then appears as a state with quasi-long-range order in composite degrees of freedom consisting of Ising-symmetry charges attached to Ising-symmetry fluxes.
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