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Chinese Physics Letters

Thermal Entanglement in the Anisotropic Heisenberg XYZ Model with Different Dzyaloshinskii–Moriya Couplings

Da-Chuang Li, Zhuo‐Liang Cao

Published Feb 1, 2009• 12 citations
Publisher

Abstract

Thermal entanglement is investigated in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii–Moriya (DM) couplings. It is shown that different DM interaction parameters have different influences on the entanglement and the critical temperature. In addition, according to the relation between the real coupling coefficients J x and J z , a more efficient DM control parameter can be obtained by adjusting the direction of DM interaction.

DOI
10.1088/0256-307x/26/2/020309

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Thermal entanglement is investigated in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii–Moriya (DM) couplings. It is shown that different DM interaction parameters have different influences on the entanglement and the critical temperature. In addition, according to the relation between the real coupling coefficients J x and J z , a more efficient DM control parameter can be obtained by adjusting the direction of DM interaction.
The thermal entanglement is investigated in a two-qubit Heisenberg XXZ system with Dzyaloshinskii–Moriya (DM) interaction. It is shown that the entanglement can be efficiently controlled by the DM interaction parameter and coupling coefficient J z . D x (the x -component parameter of the DM interaction) has a more remarkable influence on the entanglement and the critical temperature than D z (the z -component parameter of the DM interaction). Thus, by changing the DM interaction direction, we can get a more efficient control parameter to increase the entanglement and the critical temperature.
In this paper, we study the thermal entanglement in a two-qubit Heisenberg XYZ system with different Dzyaloshinskii–Moriya (DM) couplings. We show that different DM coupling parameters have different influences on the entanglement and the critical temperature. In addition, we find that when Ji (i-component spin coupling interaction) is the largest spin coupling coefficient, Di (i-component DM interaction) is the most efficient DM control parameter, which can be obtained by adjusting the direction of DM interaction.
In this paper, we study the property of thermal entanglement in four-qubit Heisenberg model, where Dzyaloshinskii-Moriya (DM) interaction is considered, and investigate the pairwise concurrences of two nearest-neighbor qubits and two next-neighbor qubits to study this entanglement property. The result shows that for the two-next-neighbor-qubit case, there exists pairwise concurrence neigher in ferromagnetic model nor in antiferromagnetic model; but for the two-nearest-neighbor-qubits case, the DM interaction and the parameter of the anisotropy exchange coupling have a significant influence on the pairwise entanglement and critical temperature Tc. Moreover, the pairwise concurrence will decrease with the increase of temperature. When the temperature execeds its critical value, the pairwise concurrence disappears. Therefore, the pairwise entanglement can be controlled and enhanced by choosing the appropriate parameters of the DM interaction and the anisotropy exchange coupling.
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.
Thermal entanglement of a(1/2,1) mixed-spin Heisenberg XXZ model in the presence of Dzyaloshinski-Moriya(DM) interaction and anisotropy Δ is investigated.It is shown that the thermal entanglement and the critical temperature can be efficiently controlled by adjusting the DM interaction parameter and anisotropy coefficient Δ.Thus,by changing the values of DM interaction and anisotropy coefficient Δ,we can get a more efficient control parameter to increase the entanglement and expand the steady value region to slow down the decreace of the entanglement.
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.