Bipartite entanglement and entropic boundary law in lattice spin systems

We investigate bipartite entanglement in spin-1∕2 systems on a generic lattice. For states that are an equal superposition of elements of a group G of spin flips acting on the fully polarized state 0⟩^, we find that the von Neumann entropy depends only on the boundary between the two subsystems A and B. These states are stabilized by the group G. A physical realization of such states is given by the ground state manifold of the Kitaev's model on a Riemann surface of genus g. For a square lattice, we find that the entropy of entanglement is bounded from above and below by functions linear in the perimeter of the subsystem A and is equal to the perimeter (up to an additive constant) when A is convex. The entropy of entanglement is shown to be related to the topological order of this model. Finally, we find that some of the ground states are absolutely entangled, i. e. , no partition has zero entanglement. We also provide several examples for the square lattice.