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International Journal of Modern Physics B

THERMAL ENTANGLEMENT IN THE ANISOTROPIC XXZ MODEL UNDER AN INHOMOGENEOUS MAGNETIC FIELD

WU Ke-dong, Bin Zhou

Published Jun 8, 2006• 2 citations
Publisher

Abstract

We investigate the thermal entanglement in the two-qubit anisotropic XXZ model in the presence of an external inhomogeneous magnetic field along the z axis. Concurrence, the measurement of entanglement is calculated. The effects of the anisotropic parameter Δ on the thermal entanglement are studied carefully for both the antiferromagnetic and ferromagnetic cases. The critical temperature Tc can also be controlled by the anisotropic parameter Δ.

DOI
10.1142/s0217979206034583

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Thermal entanglement is investigated in a two-qubit Heisenberg XY model with different inhomogeneous magnetic fields. It is found that the entanglement is dependent on the magnetic field, and the magnetic fields along different axes have different control efficiencies of entanglement. In addition, no matter in antiferromagnetic model or in ferromagnetic model, according to the relation between spin–spin coupling coefficients, the more efficient control parameters of entanglement can be obtained by adjusting the direction of external magnetic fields.
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The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.
We study the entanglement of thermal and ground states in the Heisenberg XY spin chain with an inhomogeneous magnetic field.A general result is found that for two-qubit case,pairwise entanglement is independent of the sign of coupling constant J,magnetic field B,anisotropic parameter γ and inhomogeneous parameter b of the magnetic field.At zero absolute temperature,an analytical expression of concurrence C is given through which we show that the critical magnetic field Bc increases with the increase of inhomogeneity.At finite temperature,we show analytically for the isotropic case and numerically for the anisotropic case that the thermal entanglement can be apparently enhanced by introducing the inhomogeneity of the magnetic field.We also show that for isotropic case the critical temperature Tc is alone an increasing function of the inhomogeneous parameter b,while for anisotropic case,it is determined by both B and b.