Entangling power of permutation invariant quantum states

We investigate the von Neumann entanglement entropy as function of the size of a subsystem for permutation invariant ground states in models with finite number of states per site, e.g., in quantum spin models. We demonstrate that the entanglement entropy of n sites in a system of length L generically grows as sigma log(2)[2 pi en(L-n)/L]+C, where sigma is the on-site spin and C is a function depending only on magnetization