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Chinese Physics Letters

Thermal Entanglement in a Two-Qutrit Spin-1 Anisotropic Heisenberg Model

Erhan Albayrak

Published Feb 1, 2011• 4 citations
Publisher

Abstract

The negativity ( N ) as a measure of thermal entanglement (TE) is studied for a two-qutrit spin-1 anisotropic Heisenberg XXZ chain with Dzyaloshinskii—Moriya (DM) interaction in an inhomogeneous magnetic field in detail. The effects of the DM interaction parameter D z on the thermal variation of the N for given values 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 are obtained. It is found that N persists to higher values and to higher temperatures for the higher values of ± D z and for the higher positive values of J z , i.e. in the antiferromagnetic (AFM) case. When J z < 0, the ferromagnetic (FM) case, and D z is small, and if J z is strong enough to compete with D z , N decreases. In addition, N declines with the increasing values of B and b .

DOI
10.1088/0256-307x/28/2/020306

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The negativity ( N ) as a measure of thermal entanglement (TE) is studied for a two-qutrit spin-1 anisotropic Heisenberg XXZ chain with Dzyaloshinskii—Moriya (DM) interaction in an inhomogeneous magnetic field in detail. The effects of the DM interaction parameter D z on the thermal variation of the N for given values 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 are obtained. It is found that N persists to higher values and to higher temperatures for the higher values of ± D z and for the higher positive values of J z , i.e. in the antiferromagnetic (AFM) case. When J z < 0, the ferromagnetic (FM) case, and D z is small, and if J z is strong enough to compete with D z , N decreases. In addition, N declines with the increasing values of B and b .
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 .
The thermal entanglement in a two-qubit anisotropic Heisenberg XXZ system, also XYZ system, with Dzyaloshinskii-Moriya (DM) couplings in an inhomogenous magnetic field, was studied. The effects of these two kinds of anisotropies on the thermal entanglement have been studied in detail in the concept for concurrence, the measure of entanglement. The analytical expressions of concurrence are obtained for this model. It is found that the DM interaction can enhance thermal entanglement and can be efficiently controlled by the DM interaction parameter and ehchange interaction Jx, Jy and Jz. When D is large enough, the entanglement can exist for larger temperatures and strong magnetic field. We also analysed thermodynamic properties of Heisenberg model and the most important results were shown in the paper.
The effects of the different Dzyaloshinskii—Moriya (DM) interaction on thermal entanglement of a two-qutrit Heisenberg XX spin chain in a nonuniform magnetic field are investigated. Our results imply that the x-component DM interaction plays a central role in enhancing quantum entanglement and it has a higher critical temperature than the z-component DM interaction. The entanglement can be tunable controlled by changing the multiple of the magnetic fields B 1 and B 2 . Also we found that different DM interaction are competitive to each other in some conditions.
We have studied the symmetric and non-symmetric pairwise ground state and thermal entanglement in three-qubits system. We have considered the anisotropic Heisenberg (XXZ) model in the presence of Dzyaloshinskii–Moriya (DM) interaction in addition to the Ising model in a magnetic field with DM interaction. We have found that the increment of DM interaction and magnetic field can enhance and reduce the entanglement of the system. We have shown that the non-symmetric pairwise state has higher value concurrence and critical temperature (above which the entanglement vanishes) than the symmetric pairwise one. For the negative anisotropy, the non-symmetric entanglement is a monotonic function of DM interaction while for positive anisotropy, it has a maximum versus DM parameter and vanishes for larger values of DM interaction. The conditions for the existence of thermal entanglement are discussed in detail. The most remarkable result appears at zero temperature where the three-qubits ground state entanglement of the system (in spite of two-qubits counterpart) shows the fingerprint of the quantum phase transition for a system of infinite number of qubits.
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.
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 .