Multi-boundary entanglement in Chern-Simons theory with finite gauge groups

• URL: http://arxiv.org/abs/2003.01404v2
• Date: Thu, 23 Apr 2020 17:12:52 GMT
• Title: Multi-boundary entanglement in Chern-Simons theory with finite gauge groups
• Authors: Siddharth Dwivedi, Andrea Addazi, Yang Zhou, Puneet Sharma
• Abstract summary: In (1+1)-$d$, we focus on the states associated with torus link complements which live in the tensor product of Hilbert spaces associated with multiple $T2$. 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 $T2$.
• Score: 5.100636992246072
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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. $\text{EE}(G_1 \times G_2) = \text{EE}(G_1)+\text{EE}(G_2)$. 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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