Thermal entanglement of spins in mean-field clusters

Abstract

We determine thermal entanglement in mean field clusters of $N$ spin one-half particles interacting via the anisotropic Heisenberg interaction, with and without external magnetic field. For the $xxx$ cluster in the absence of magnetic field we prove that only the N=2 ferromagnetic cluster shows entanglement. An external magnetic field $B$ can only entangle $xxx$ anti-ferromagnetic clusters in certain regions of the $B-T$ plane. On the other hand, the $xxz$ clusters of size $N>2$ are entangled only when the interaction is ferromagnetic. Detailed dependence of the entanglement on various parameters is investigated in each case.

16 pages, 11 figures

References in corpus (6)

• Entanglement in a second order quantum phase transition
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Entanglement in a first order quantum phase transition
• Concurrence in collective models
• Thermal entanglement properties of small spin clusters
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Cited by in corpus (3)

• Experimental Determination of Thermal Entanglement in Spin Clusters using Magnetic Susceptibility Measurements
• Entanglement in a Time-Dependent Coupled XY Spin Chain in an External Magnetic Field
• Magnetic Properties and Thermal Entanglement on a Triangulated Kagome Lattice