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

Abstract

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 $s\ensuremath{\le}5/2$ (with $N\ensuremath{\le}8$). 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.