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

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

2009-12-23

arxiv.org/abs/0912.4733v2

J. Phys. A 43, 185304 (2010)

Physics

Condensed Matter

Statistical Mechanics

11 pages, 3 figures

Scientific paper

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 $S^z_T=\pm 1$ and $S^z_T=0$ 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.

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