Thermal entanglement properties of small spin clusters

TL;DR

This paper analytically investigates the entanglement properties of small spin clusters, specifically a spin tetramer, and relates these quantum features to magnetic properties and phase transitions, with applications to real compounds like V12.

Contribution

It provides analytical calculations of ground and thermal state entanglement in a spin tetramer with various interactions, linking entanglement measures to experimental magnetic data.

Findings

Signatures of quantum phase transitions identified via entanglement measures.

Lower bounds of critical entanglement temperature estimated from susceptibility.

Entanglement temperatures for bipartite and multipartite entanglement determined.

Abstract

Exchange interactions in spin systems can give rise to quantum entanglement in the ground and thermal states of the systems. In this paper, we consider a spin tetramer, with spins of magnitude 1/2, in which the spins interact via nearest-neighbour, diagonal and four-spin interactions of strength J1, J2 and K respectively. The ground and thermal state entanglement properties of the tetramer are calculated analytically in the various limiting cases. Signatures of quantum phase transition (QPT) in terms of appropriate entanglement measures are obtained. The magnetic properties of a S = 1/2 AFM polyoxovanadate compound, V12, are well explained by spin tetramers with only nearest-neighbour exchange interactions. Treating the magnetic susceptibility chi as an entanglement witness (EW), an estimate of the lower bound of the critical entanglement temperature, T_c, above which the multipartite entanglement disappears in the experimental compound, is determined. A second EW based on energy provides an estimate of the entanglement temperature T_E, below which bipartite entanglement is certainly present in the system, is determined. The cases of the symmetric trimer and the tetrahedron are also considered.