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The scaling of entanglement entropy for the nearest neighborantiferromagnetic Heisenberg spin model is studied computationally for clustersjoined by a single bond. Bisecting the balanced three legged Bethe Cluster,gives a second Renyi entropy and the valence bond entropy which scales as thenumber of sites in the cluster. For the analogous situation with squareclusters, i.e. two $L \times L$ clusters joined by a single bond, numericalresults suggest that the second Renyi entropy and the valence bond entropyscales as $L$. For both systems, the environment and the system are connectedby the single bond and interaction is short range. The entropy is not constantwith system size as suggested by the area law.

Scaling of Entanglement Entropy for the Heisenberg Model on Clusters Joined by Point Contacts