Symmetry-resolved entanglement in symmetry-protected topological phases
Symmetry-resolved entanglement in symmetry-protected topological phases
复制标题
对称保护拓扑相中的对称解决纠缠
DOI：
10.1103/physrevb.102.235157
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发表时间：
2020
影响因子：
3.7
通讯作者：
E. Sela
中科院分区：
文献类型：
--
作者：
Daniel Azses;E. Sela
对称保护拓扑相在一维纠缠谱中具有普遍简并性。本文在“对称分辨纠缠”的框架下，利用上同调理论对这一现象进行了表述。我们开发了一种计算任意维spt纠缠度量的通用方法，特别是通过具有广义缺陷的多片黎曼曲面上的离散路径积分来计算对称分辨纠缠（SRE）。由此得到的非平凡流形上的路径积分用描述spt拓扑作用的群环来表示。它们的上同调分类允许识别通用纠缠特性。具体来说，我们证明了在有限阿贝尔酉对称保护下的所有一维拓扑相的纠缠均分。这种方法为探索更高的维度和额外的对称性开辟了道路。
Symmetry protected topological phases (SPTs) have universal degeneracies in the entanglement spectrum in one dimension (1D). Here, we formulate this phenomenon in the framework of "symmetry resolved entanglement" using cohomology theory. We develop a general approach to compute entanglement measures of SPTs in any dimension and specifically symmetry resolved entanglement (SRE) via a discrete path integral on multi-sheet Riemann surfaces with generalized defects. The resulting path integral on nontrivial manifolds is expressed in terms of group cocycles describing the topological actions of SPTs. Their cohomology classification allows to identify universal entanglement properties. Specifically, we demonstrate entanglement equipartition for all 1D topological phases protected by finite abelian unitary symmetries. The method opens the way to explore higher dimensions and additional symmetries.