Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
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有限规范群陈-西蒙斯理论中的多边界纠缠
DOI：
10.1007/jhep04(2020)158
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发表时间：
2020-03
影响因子：
5.4
通讯作者：
Puneet Sharma
中科院分区：
文献类型：
--
作者：
Siddharth Dwivedi;Andrea Addazi;Yang Zhou;Puneet Sharma
我们研究在具有有限离散规范群\(G\)的\((1 + 1)\)维和\((2 + 1)\)维陈 - 西蒙斯理论中制备的态的多边界纠缠结构。\((1+1)\)维中的态与亏格为\(g\)且具有多个\(S^1\)边界的黎曼曲面相关联。
We study the multi-boundary entanglement structure of the states prepared in (1+1) and (2+1) dimensional Chern-Simons theory with finite discrete gauge group G. The states in (1+1)-d are associated with Riemann surfaces of genus g with multiple S
1 boundaries and we use replica trick to compute the entanglement entropy for such states. In (2+1)-d, we focus on the states associated with torus link complements which live in the tensor product of Hilbert spaces associated with multiple T
2. We present a quantitative analysis of the entanglement structure for both abelian and non-abelian groups. For all the states considered in this work, we find that the entanglement entropy for direct product of groups is the sum of entropy for individual groups, i.e. EE(G
1
× G
2) = EE(G
1) + EE(G
2). Moreover, the reduced density matrix obtained by tracing out a subset of the total Hilbert space has a positive semidefinite partial transpose on any bi-partition of the remaining Hilbert space.
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