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.

arXiv comment16 pages, 11 figures

References in corpus (25)

• Entanglement of Formation of an Arbitrary State of Two Qubits
• Quantum Computation with Quantum Dots
• Entanglement of a Pair of Quantum Bits
• Universal Quantum Computation with the Exchange Interaction
• Entangled Rings
• Entanglement in a second order quantum phase transition
• Thermal concurrence mixing in a 1D Ising model
• Finite-Size Scaling Exponents of the Lipkin-Meshkov-Glick Model
• Continuous unitary transformations and finite-size scaling exponents in the Lipkin-Meshkov-Glick model
• Quantum entanglement and Bell inequalities in Heisenberg spin chains
• Entanglement entropy in the Lipkin-Meshkov-Glick model
• Thermal and ground-state entanglement in Heisenberg XX qubit rings
• Anisotropic exchange interaction of localized conduction-band electrons in semiconductor structures
• Entanglement in a first order quantum phase transition
• Threshold temperature for pairwise and many-particle thermal entanglement in the isotropic Heisenberg model
• Thermal entanglement in three-qubit Heisenberg models
• Thermal entanglement of spins in a nonuniform magnetic field
• Cancellation of Spin-Orbit Effects in Quantum Gates Based on the Exchange Coupling in Quantum Dots
• Quantum Information Processing with Ferroelectrically Coupled Quantum Dots
• Concurrence in collective models
• Impurity Scattering Induced Entanglement of Ballistic Electrons
• Thermal entanglement properties of small spin clusters
• Universal Quantum Logic from Zeeman and Anisotropic Exchange Interactions
• Thermal entanglement of spins in the Heisenberg model at low temperatures
• Separability conditions and limit temperatures for entanglement detection in two qubit Heisenberg XYZ models

Cited by in corpus (6)

• Experimental Determination of Thermal Entanglement in Spin Clusters using Magnetic Susceptibility Measurements
• Magnetic and quantum entanglement properties of the distorted diamond chain model for azurite
• Entanglement in a Time-Dependent Coupled XY Spin Chain in an External Magnetic Field
• Magnetic Properties and Thermal Entanglement on a Triangulated Kagome Lattice
• Quantifying quantum coherence in a metal-silicate framework
• Entanglement Transfer via XXZ Heisenberg chain with DM Interaction