Energy as a witness of multipartite entanglement in chains of arbitrary spins

We develop a general approach for deriving the energy minima of biseparable states in chains of arbitrary spins s, and we report numerical results for spin values s<=5/2 (with N<=8). The minima provide a set of threshold values for exchange energy that allow us to detect different degrees of multipartite entanglement in one-dimensional spin systems. We finally demonstrate that the Heisenberg exchange Hamiltonian of N spins has a nondegenerate N-partite entangled ground state, and it can thus witness such correlations in all finite spin chains.