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Negativity of Heisenberg XY Model

Siping Liu

Published Jan 1, 2010• 0 citations
OpenAlex

Abstract

Using a universal entanglement measure,negativity,we investigate the thermal entanglement of two-qubit Heisenberg XY model in thermal equilibrium at temperature T in the presence of an external magnetic field B.When anisotropy parameter γ is large enough there occurs a revival of the entanglement.By adjusting the magnetic field B,one can produce entanglement for any finite T.For isotropic case there is no entanglement above a critical temperature that is independent of the external B field.

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Using a universal entanglement measure,negativity,we investigate the thermal entanglement of two-qubit Heisenberg XY model in thermal equilibrium at temperature T in the presence of an external magnetic field B.When anisotropy parameter γ is large enough there occurs a revival of the entanglement.By adjusting the magnetic field B,one can produce entanglement for any finite T.For isotropic case there is no entanglement above a critical temperature that is independent of the external B field.
We investigate the entanglement of a two-qubit anisotropic Heisenberg XY chain in thermal equilibrium at temperature T in the presence of an external magnetic field B along the z axis. By means of the combined influences of anisotropic interactions and a magnetic field B, one is able to produce entanglement for any finite T, by adjusting the magnetic field strength. This contrasts with the isotropic interaction or the B = 0 cases, for which there is no entanglement above a critical temperature T(c) that is independent of the external B field.
Negativity is an universal entanglement measure.The entanglement of two-party quantum system can be easily calculated with negativity.The thermal entanglement in the two qubit anisotropic Heisenberg XXZ model is studies by means of Negativity.The influence of temperature T and an external magnetic field B on the entanglement is investigated in thermal equilibrium.When the temperature is less than an critical temperature TC,the thermal entanglement is depended on the magnetic field strength,otherwise the entanglement disappears.
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.
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.
Thermal entanglement of a two-qubit Heisenberg XYZ chain is studied.It is found that the ground state entanglement maintains a maximal constant until it drops suddenly at a critical magnetic field.Increasing the value of can extend the entanglement region in terms of temperature and magnetic field.At a finite temperature,increasing the anisotropy parameter can enhance and extend the revival entanglement when the magnetic field is beyond the critical point.These results may provide theoretical proof for manipulating the entanglement with magnetic field,strength of interaction and anisotropy parameter.