Entanglement in simple spin networks with a boundary

Abstract

We investigate the bipartite entanglement for the boundary states in a simple type of spin networks with dangling edges, in which the two complementary parts are linked by two or more edges. Firstly, the spin entanglement is considered in the absence of the intertwiner entanglement. By virtue of numerical simulations, we find that the entanglement entropy usually depends on the group elements. More importantly, when the intertwiner entanglement is taken into account, we find that it is in general impossible to separate the total entanglement entropy into the contribution from spins on edges and the contribution from intertwiners at vertices. These situations are in contrast to the case when the two vertices are linked by a single edge.