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

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.

arXiv comment50 pages, 8 figures, matches with the published version

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Cited by in corpus (5)

• Entanglement Classification from a Topological Perspective
• Semiclassical limit of topological Rényi entropy in $3d$ Chern-Simons theory
• Topological entanglement and hyperbolic volume
• Large-party limit of topological entanglement entropy in Chern-Simons theory
• Topological entanglement and number theory