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Chinese Physics Letters

Thermal Entanglement in the Spin- S Heisenberg XYZ Model

Hu Li, Da-Chuang Li, Xianping Wang, Ming Yang, Zhuo‐Liang Cao

Published Apr 1, 2014• 2 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/31/4/040301

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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.
The effects of spin-spin interaction on thermal entanglement of a two-qubit Heisenberg XYZ model with different inhomogeneous magnetic fields are investigated. It is shown that the entanglement is dependent on the spin-spin interaction and the inhomogeneous magnetic fields. The larger the J i (i-axis spin-spin interaction), the higher critical value the B i (i-axis uniform magnetic field) has. Moreover, in the weak-field regime, the larger J i corresponds to more entanglement, while in the strong-field regime, different J i correspond to the same entanglement. In addition, it is found that with the increase of J i , the concurrence can approach the maximum value more rapidly for the smaller B i , and can reach a larger value for the smaller b i (i-axis nonuniform magnetic field). So we can get more entanglement by increasing the spin-spin interaction J i , or by decreasing the uniform magnetic field B i and the nonuniform magnetic field b i .
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.
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.
We study the entanglement of a two-qubit one-dimensional XYZ Heisenberg chain in thermal equilibrium at temperature T. We obtain an analytical expression for the concurrence of this system in terms of the parameters of the Hamiltonian and T. We show that depending on the relation among the coupling constants, it is possible to increase the amount of entanglement of the system by increasing its anisotropy. We also show numerically that for all sets of the coupling constants entanglement is a monotonically decreasing function of the temperature T, proving that we must have at least an external magnetic field in the z-direction to obtain a behavior where entanglement increases with T.
In this paper we study the effect of temperature, magnetic field, and exchange coupling on the thermal entanglement in a spin chain which consist of two qubits and one qutrit.We use negativity as a measure of entanglement in our study.We apply magnetic field, uniform and nonuniform field, on it.The results show that the entanglement decreases with increase in temperature.Also, we have found that under a magnetic field, either uniform or nonuniform, in constant temperature, the entanglement decreases.We have found that increasing exchange coupling of any two particles decreases the entanglement of the other two particles.Finally, we have compared our system with a two-particle system and found that in presence of a magnetic field the increase in number of particles leads to the decrease in the entanglement.