Exact results for the bipartite entanglement entropy of the AKLT spin-1 chain

We study the bipartite entanglement between a subsystem of size l and the rest of the system of total size L as it occurs in a spin-1 Affleck-Kennedy-Lieb-Tasaki (AKLT) chain subject to open boundary conditions. In this case, the ground-state manifold is four-fold degenerate and there is strong dependence on the parity of the number of spins, L. We present exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the subsystem, l, and the total system size, L, for all four degenerate ground states for both odd and even L. In the large l, L limits the entanglement entropy approaches ln (2) for the SzT = ±1 while it approaches twice that value, 2ln (2), for the SzT = 0 states. In all cases, it is found that this constant is approached exponentially fast defining a length scale ξ = 1/ln (3) equal to the known bulk correlation length.