Detection through exchange energy of multipartite entanglement in spin rings

TL;DR

This paper demonstrates that exchange energy can serve as an effective witness for multipartite entanglement in antiferromagnetic spin rings, enabling both global and spin-specific entanglement detection.

Contribution

It introduces a general method to identify multipartite entanglement via exchange energy and applies it to spin rings with and without magnetic defects.

Findings

Non-degenerate ground states of even-spin rings are N-partite entangled.

Exchange energy can detect entanglement in the presence of magnetic defects.

Numerical results support the use of exchange energy as an entanglement witness.

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.