The effects of spin-spin interaction on thermal entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the J i (i-axis spin-spin interaction), the higher critical value the B i (i-axis uniform magnetic field) has. Moreover, in the weak-field regime, the larger J i corresponds to more entanglement, while in the strong-field regime, different J i correspond to the same entanglement. In addition, it is found that with the increase of J i , the concurrence can approach the maximum value more rapidly for the smaller B i , and can reach a larger value for the smaller b i (i-axis nonuniform magnetic field). So we can get more entanglement by increasing the spin-spin interaction J i , or by decreasing the uniform magnetic field B i and the nonuniform magnetic field b i .
The thermal entanglement in the spin-S Heisenberg XYZ model is studied in detail by using the entanglement measure of negativity. The effects of spin on the thermal entanglement, the threshold temperature, the critical uniform external magnetic field, the nonuniform external magnetic field and the entanglement extremum are discussed, respectively. It is shown that with increasing spin, the entanglement will increase, and then decrease slowly. In addition, we find that entanglement will approach a constant N c with the increase of DM interaction, the constant increases with the increase of spin, and both the threshold temperature T c and critical uniform external magnetic field B c will increase with the increasing spin. Thus high-spin system can inhibit the influence of the external environment better.
The thermal entanglement in a two-qubit Heisenberg
XXZ spin chain is investigated under an inhomogeneous magnetic field
b. We show that the ground-state entanglement is independent of the interaction of
z-component
Jz. The thermal entanglement at the fixed temperature can be enhanced when
Jz increases. We strictly show that for any temperature
T and
Jz, the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field
bc is independent of
Jz. The critical magnetic field
Bc increases with the increasing $\ensuremath{\mid}b\ensuremath{\mid}$ but the maximum entanglement value that the system can arrive at becomes smaller.
We investigate the thermal entanglement of a two-qubit anisotropic Heisenberg XYZ model with both uniform and nonuniform magnetic fields in the x-z plane at thermal equilibrium. For the uniform magnetic field case, it is shown that the value of the critical magnetic field B(subscript c) may be broadened by changing the direction of the magnetic field and that the revival of entanglement is due to the combined influence of the magnetic field and the Heisenberg model's partial anisotropy in the plane which is perpendicular to the magnetic field. Moreover, the direction of the magnetic field will have an effect on the critical temperature T(subscript c) only when the field strength is large enough. For the nonuniform magnetic field case it is found that, for any direction of the magnetic field, the introduction of inhomogeneity in the magnetic field always broadens the critical magnetic field B(subscript c), but diminishes the maximum entanglement.
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.
The role of spin-orbit interaction in the ground state and thermal entanglement of a Heisenberg
XYZ two-qubit system in the presence of an inhomogeneous magnetic field is investigated. We show that the ground state entanglement tends to vanish suddenly for a certain value of the spin-orbit parameter
D and, when
D crosses its critical value
Dc, the entanglement undergoes a revival. Indeed, when
D crosses its critical value
(Dc), the ground state entanglement tends to its maximum value
(C=1). Also, at finite temperatures there are revival regions in the $D\text{\ensuremath{-}}T$ plane. In these regions, entanglement first increases with increasing temperature and then decreases and ultimately vanishes for temperatures above a critical value. We find that this critical temperature is an increasing function of
D and that the amount of entanglement in the revival region depends on the spin-orbit parameter. Therefore when spin-orbit interaction is included larger thermal entanglement can exist at higher temperatures. We also show that the rate of enhancement of thermal entanglement by
D is not the same for ferromagnetic
(Jz<0) and antiferromagnatic
(Jz>0) chains. The entanglement teleportation via the quantum channel constructed by the above system is also investigated, and the influence of the spin-orbit interaction on the fidelity of teleportation and entanglement of replica states is studied. We show that, by introducing spin-orbit interaction, the entanglement of the replica state and fidelity of teleportation can be increased for the case of
Jz<0. We also argue that a minimal entanglement of the channel is required to realize efficient entanglement teleportation and, in the case of
Jz<0, this minimal entanglement can be achieved by introducing spin-orbit interaction.