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Science in China. Series G, Physics, mechanics & astronomy/Science in China. Series G, Physics, Mechanics & Astronomy

Thermal entanglement in a mixed-spin Heisenberg XXZ model under a nonuniform external magnetic field

Jia Hong

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

The thermal entanglement in (1/2,1) mixed-spin Heisenberg XXZ model is investigated under an external nonuniform magnetic field. In the uniform magnetic field system,the critical magnetic field Bc and critical temperature Tc are increased by increasing the anisotropic parameter k. The degree of magnetic field b plays an important role in improving the critical temperature and enlarging the region of entan-glement in the nonuniform magnetic field system.

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The thermal entanglement in (1/2,1) mixed-spin Heisenberg XXZ model is investigated under an external nonuniform magnetic field. In the uniform magnetic field system,the critical magnetic field Bc and critical temperature Tc are increased by increasing the anisotropic parameter k. The degree of magnetic field b plays an important role in improving the critical temperature and enlarging the region of entan-glement in the nonuniform magnetic field system.
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In contrast to the spin-half Heisenberg model, we investigate the effects of anisotropy and external magnetic field on thermal entanglement in a (1/2,1) mixed-spin Heisenberg model. By using the concept of negativity, we find the critical temperature T c and critical magnetic field B c of mixed-spin are much higher than that of spin-half, and this phenomenon is more evident with increasing anisotropy coefficient Δ. Contrary to the spin-half, we also observe that the nonuniform field can enhance the entanglement of mixed-spin to a great extent.
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.
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.
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.