Exact Results for the Bipartite Entanglement Entropy of the AKLT spin-1 chain

Abstract

We study the entanglement between two domains of a spin-1 AKLT chain subject to open boundary conditions. In this case the ground-state manifold is four-fold degenerate. We summarize known results and present additional exact analytical results for the von Neumann entanglement entropy, as a function of both the size of the domains and the total system size for {\it all} four degenerate ground-states. In the large $l,L$ limit the entanglement entropy approaches $\ln (2)$ and $2\ln (2)$ for the $S_T^z=\pm 1$ and $S_T^z=0$ states, respectively. In all cases, it is found that this constant is approached exponentially fast defining a length scale $\xi =1/\ln (3)$ equal to the known bulk correlation length.

11 pages, 3 figures

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