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Journal of Jianghan University

Thermal Entanglement of Heisenberg XXZ Model

Siping Liu

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
In this paper, the entanglement in a spin-1 Heisenberg XXZ chain with uniform and nonuniform external magnetic field is investigated in the terms of the measure of entanglement called 'negativity'. The effects of the external magnetic field, the anisotropy parameter and the temperature on the negativity are discussed respectively. It can be seen that the entanglement in this spin chain for any temperature is symmetric with respect to zero magnetic field. We calculate the partially transposed density matrix and give qualitatively results at different temperatures. In order to show the results clearly, the behavior of negativity is presented for five different cases. It can be found that the temperature and the external magnetic field can effect the feature of the thermal entanglement significantly. In addition, under certain condition, the negativity may be enhanced under a nonuniform magnetic field.
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.