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 S1 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 T2. 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(G1× G2) = EE(G1) + EE(G2). 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.
Highlights
The study of entanglement in quantum field theory (QFT) has been an active area of research and is yet far from complete
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
We studied the entanglement structure of multi-boundary states prepared in Chern-Simons theory with a finite discrete gauge group
Summary
The study of entanglement in quantum field theory (QFT) has been an active area of research and is yet far from complete. A typical path integral picture has been shown in figure 1(a) where the boundary ∂M has been bi-partitioned into connected regions A and its complement A Another novel approach to study entanglement is to consider these theories on manifolds whose boundary itself consists of disconnected or disjoint components as shown in figure 1(b). We will study the salient features of multi-boundary entanglement structures in Chern-Simons theory with finite discrete gauge groups. If we consider two topologically different manifolds M and M with the same boundary ∂M = ∂M , the corresponding Chern-Simons partition functions for a particular gauge group will, in principle, give two different states |Ψ and |Ψ in the same Hilbert space H∂M. The aim of the present work is to study the entanglement structure of the states constructed in Chern-Simons theory with finite discrete gauge groups.
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