Abstract
We study the structure of entanglement in a supersymmetric lattice model of fermions on certain types of decorated graphs with quenched disorder. In particular, we construct models with controllable ground state degeneracy protected by supersymmetry and the choice of Hilbert space. We show that in certain special limits these degenerate ground states are associated with local impurities and that there exists a basis of the ground state manifold in which every basis element satisfies a boundary law for entanglement entropy. On the other hand, by considering incoherent mixtures or coherent superpositions of these localized ground states, we can find regions that violate the boundary law for entanglement entropy over a wide range of length scales. More generally, we discuss various desiderata for constructing violations of the boundary law for entanglement entropy and discuss possible relations of our work to recent holographic studies.
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