Entanglement in spin chains and lattices with long-range Ising-type interactions -: art. no. 097203

We consider N initially disentangled spins, embedded in a ring or d-dimensional lattice of arbitrary geometry, which interact via some long-range Ising-type interaction. We investigate relations between entanglement properties of the resulting states and the distance dependence of the interaction in the limit N -> infinity. We provide a sufficient condition when bipartite entanglement between blocks of L neighboring spins and the remaining system saturates and determine S-L analytically for special configurations. We find an unbounded increase of S-L as well as diverging correlation and entanglement length under certain circumstances. For arbitrarily large N, we can efficiently calculate all quantities associated with reduced density operators of up to ten particles.