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Chinese Physics B

Thermal entanglement in a two-qubit HeisenbergXYchain with the Dzyaloshinskii–Moriya interaction

Qin Meng, Xu Sheng-Long, Tao Ying-Juan, Tian Dong-Ping

Published Aug 1, 2008• 14 citations
Publisher

Abstract

This paper investigates thermal entanglements of a two-qubit Heisenberg XY chain in the presence of the Dzyaloshinskii–Moriya anisotropic antisymmetric interaction. By the concept of concurrence, it is found that the effects of spin–orbit coupling on the entanglement are different from those of spin–spin model. The analytical expressions of concurrence are obtained for this model.

DOI
10.1088/1674-1056/17/8/009

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This paper investigates thermal entanglements of a two-qubit Heisenberg XY chain in the presence of the Dzyaloshinskii–Moriya anisotropic antisymmetric interaction. By the concept of concurrence, it is found that the effects of spin–orbit coupling on the entanglement are different from those of spin–spin model. The analytical expressions of concurrence are obtained for this model.
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Thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of different Dzyaloshinskii–Moriya (DM) anisotropic antisymmetric interactions and entanglement teleportation using two independent Heisenberg chains as quantum channel are investigated. It is found that the anisotropic coupling coefficient Jz (z-component exchange constant) and DM interactions can excite the entanglement, and x-component DM interaction Dx has a more remarkable influence than the z-axis DM interaction Dz for exchange constant J > 0 (antiferromagnetic) case, which is contrary to coupling coefficient J < 0 (ferromagnetic) case. The output entanglement and fidelity increase with increasing z-axis coupling parameter Jz for both the antiferromagnetic J > 0 case and ferromagnetic J < 0 case. By introducing the different DM interactions, it is superior to teleportate initial state by using the Dz interaction in the model for J > 0 case. But for J < 0 case, the Dx interaction is better, and the output concurrence and fidelity can reach the maximum value 1 with suitable Dx.
We studied the properties of thermal entanglement in one-dimention two-qubit Heisenberg model,where Dzyaloshinskii-Moriya(DM) interaction between spin with x-component and y-component was considered and concurrence was calculated to research this entanglement property.The results showed that on the case of ferromagnetic and antiferromagnetic,interaction had different effects on the entanglement and critical temperature.Therefore,the entanglement could be controlled and enhanced by choosing appropriate interaction between x-component and y-component.
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.
This paper investigates the entanglement evolution of a two-qubit anisotropic Heisenberg XYZ chain in the presence of Dzyaloshinskii–Moriya interaction. The time evolution of the concurrence is studied for the initial pure entangled states cos θ |00⟩ + sin θ |11⟩ and cos φ |01⟩ + sin φ |10⟩ at zero temperature. The influences of Dzyaloshinskii–Moriya interaction D , anisotropic parameter Δ and environment coupling strength γ on entanglement evolution are analysed in detail. It is found that the effect of noisy environment obviously suppresses the entanglement evolution, and the Dzyaloshinskii–Moriya interaction D acts on the time evolution of entanglement only when the initial state is cos φ |01⟩ + sin φ |10⟩. Finally, a formula of steady state concurrence is obtained, and it is shown that the stable concurrence, which is independent of different initial states and Dzyaloshinskii–Moriya interaction D , depends on the anisotropic parameter Δ and the environment coupling strength γ.