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Journal of Physics A Mathematical and Theoretical

Entanglement in a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field

Ke-Tao Guo, M. M. Liang, Hong-Yu Xu, Zhu Cheng-Bo

Published Nov 22, 2010• 15 citations
Publisher

Abstract

Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.

DOI
10.1088/1751-8113/43/50/505301

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Using the concept of negativity, we investigate the thermal entanglement of a two-spin (1/2, 3/2) mixed-spin Heisenberg XXZ chain with an inhomogeneous external magnetic field. We obtain the analytical results of entanglement of this model. For the case of uniform magnetic field, we find that the critical temperature increases with the increase of the anisotropy parameter k , and for the same couplings, the critical temperature is higher than the results of the spin-1/2 XXZ chain and (1/2, 1) mixed-spin XXZ chain. Evidence of the quantum phase transition is found, and by adjusting the inhomogeneous magnetic parameter b , one is able to obtain more entanglement at higher temperature.
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.
The thermal entanglement of a two-qutrit spin-1 anisotropic Heisenberg XXZ chain in an inhomogeneous magnetic field is studied in detail. The effects of the external magnetic field ( B ), a parameter b which controls the inhomogeneity of B , and the bilinear interaction parameters J x = J y ≠ J z on the thermal variation of the negativity are studied in detail. It is found that negativity N decreases when the values of magnetic field, inhomogeneity b and temperature are increasing. In addition, N remains at higher temperatures for higher values of J z and lower values of B and b .
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.
Ground state entanglement and thermal entanglement of a two-qubit Heisenberg XXZ chain in the presence of the different Dzyaloshinski-Moriya interaction and inhomogeneous magnetic field are investigated. By the concept of concurrence, we find that the inhomogeneity of the magnetic field may make entanglement last for a long time and the critical temperature is dependent on J z and b . The entanglement can be increased by increasing the temperature in some cases. We also find that the x -component parameter D x has a higher critical temperature and more entanglement for a certain condition than the z -component parameter D z .