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Physica Scripta

Entanglement properties of a two-qubit, mixed-spin, Heisenberg chain under a nonuniform magnetic field

Guo-Hui Yang, Ling Zhou

Published Jul 31, 2008• 13 citations
Publisher

Abstract

We investigate the entanglement property of a two-qubit, mixed-spin, Heisenberg system under a nonuniform magnetic field. We show that increasing b can improve the threshold temperature, and can also make the entanglement enhanced. It is very interesting to note that the joining of the nonuniform magnetic field b can not only induce the entanglement for the ferromagnetic case, but can also make the entanglement symmetrical in terms of J for a larger value of b , while the uniform field B cannot do this. We also analyze the ground-state entanglement features in detail.

DOI
10.1088/0031-8949/78/02/025703

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We investigate the quantum entanglement of the ground state and the mixed states at finite temperatures for a two-qubit system within the framework of an anisotropic Heisenberg XYZ model in the presence of a nonuniform magnetic field. As a measure of the entanglement, the concurrence of the two-qubit states is calculated and is analysed in detail as a function of the coupling constants, magnetic field and temperature. Consequently, we show that the combined influence of the anisotropic interaction and the nonuniformity of the magnetic fields predicts much pronounced entanglement properties.
The thermal entanglement in a two-qubit Heisenberg XXZXXZXXZ spin chain is investigated under an inhomogeneous magnetic field bbb. We show that the ground-state entanglement is independent of the interaction of zzz-component Jz{J}_{z}Jz​. The thermal entanglement at the fixed temperature can be enhanced when Jz{J}_{z}Jz​ increases. We strictly show that for any temperature TTT and Jz{J}_{z}Jz​, the entanglement is symmetric with respect to zero inhomogeneous magnetic field, and the critical inhomogeneous magnetic field bc{b}_{c}bc​ is independent of Jz{J}_{z}Jz​. The critical magnetic field Bc{B}_{c}Bc​ increases with the increasing $\ensuremath{\mid}b\ensuremath{\mid}$ but the maximum entanglement value that the system can arrive at becomes smaller.
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 .
We investigate the thermal entanglement in the two-qubit Heisenberg XY model with a nonuniform magnetic field. Concurrence, the measurement of entanglement, is calculated. The behavior of concurrence is present at three different cases. Contrary to the uniform magnetic field case, we find that the entanglement and the critical temperature TC{T}_{C}TC​ may be enhanced under a nonuniform magnetic field.