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Physical Review A

Thermal entanglement in the two-qubit Heisenberg XY model under a nonuniform external magnetic field

Yang Sun, Yuguang Chen, Hong Chen

Published Oct 6, 2003• 175 citations
Publisher

Abstract

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 ${T}_{C}$ may be enhanced under a nonuniform magnetic field.

DOI
10.1103/physreva.68.044301

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We investigate the thermal entanglement of two-qubit anisotropic Heisenberg XY model in the presence of an external nonuniform magnetic field B along the z-axis. Concurrence, the measure of entanglement is calculated and its property is studied in different cases. Two best models, Ising model under a uniform magnetic and isotropic model in a nonuniform magnetic field, are discovered. In the two models, the critical temperature Tc (above which there is no entanglement) can be enhanced and its concurrence is maximal.
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.
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We investigate the thermal entanglement of Heisenberg-type coupled two-qubit system in the presence of two controllable magnetic fields (B+b) and (B-b). We find that under the condition of low temperature and uniform magnetic field, the entanglement between the two qubits exhibits platform-like behavior. By controlling the inhomogeneous magnetic field b and selecting suitable material we can optimize the thermal entanglement and enhance the critical temperature Tc of dead entanglement. We also find that the entanglement switch can be realized in a broader region of temperature by modulating the uniform field B.