Detection through exchange energy of multipartite entanglement in spin rings

Abstract: We investigate multipartite entanglement in rings of arbitrary spins with antiferromagnetic interactions between nearest neighbors. In particular, we show that the non-degenerate ground state of rings formed by an even number ($N$) of spins is $N$-partite entangled, and exchange energy can thus be used as a multipartite-entanglement witness. We develop a general approach to compute the energy minima corresponding to biseparable states, and provide numerical results for a representative set of systems. Despite its global character, exchange energy also allows a spin-selective characterization of entanglement. In particular, in the presence of a magnetic defect, one can derive separability criteria for each individual spin, and use exchange energy for detecting entanglement between this and all the other spins.