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Journal of the Korean Physical Society

Effect of the Dzyaloshinski Moria Interaction on Quantum Correlations for the XXZ Heisenberg Spin Chain

Safa Jami, Asiyeh Dehnavi

Published Mar 1, 2019• 1 citation
Publisher

Abstract

We have studied the effect of the Dzyaloshinskii Moria (DM) interaction on geometric quantum discord (GQD) and concurrence for two spin 1/2 particles in the XXZ Heisenberg model, we have also investigated the effects of the temperature, the strength of DM interaction (D) and the anisotropic coupling constant of the Heisenberg model J z on them in the GQD and concurrence. Further, we have compared the behaviors of GQD and entanglement for our system under the above parameters.

DOI
10.3938/jkps.74.434

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We have studied the effect of the Dzyaloshinskii Moria (DM) interaction on geometric quantum discord (GQD) and concurrence for two spin 1/2 particles in the XXZ Heisenberg model, we have also investigated the effects of the temperature, the strength of DM interaction (D) and the anisotropic coupling constant of the Heisenberg model J z on them in the GQD and concurrence. Further, we have compared the behaviors of GQD and entanglement for our system under the above parameters.
The thermal quantum discord (QD) is studied in a two-qubit Heisenberg XXZ system with Dzyaloshinskii-Moriya (DM) interaction. We compare the thermal QD with thermal entanglement in this system and find remarkable differences between them. For instance, we show situations where QD decreases asymptotically to zero with temperature TTT while entanglement decreases to zero at the point of critical temperature, situations where QD decreases with certain tunable parameters such as DzD_zDz​ and DxD_xDx​ when entanglement increases. We find that the characteristic of QD is exotic in this system and this possibly offers a potential solution to enhance entanglement of a system. We also show that tunable parameter DxD_xDx​ is more efficient than parameter DzD_zDz​ in most regions for controlling the QD.
In this paper, we study the improvement and manipulation of pairwise thermal entanglement in one-dimentional three-qubit Heisenberg model, where Dzyaloshinskii-Moriya （DM） interaction is considered and concurrence is calculated to research this entanglements property. The results show that for XXX model, DM interaction can induce entanglement in the antiferromagnetic and ferromagnetic spin chains although the required critical values are different for these cases. For XXZ model, by introducing DM interaction D, antiferromagnetic spin chain has entanglement which is absent when D=0, and in addition, for antiferromagnetic and ferromagnetic cases, DM interaction D and the anisotropy parameter Δ have different effects on entanglement. As a result, the entanglement can be controlled and enhanced by choosing appropriate DM interaction and anisotropy parameter. Furthermore, we find that at the same temperature, no matter for antiferromagnetic or ferromagnetic spin chains, the critical DM interaction inducing entanglement should be greater in a three-qubit XXZ model than that in a two-qubit XXZ model.
We investigate the pairwise thermal quantum discord in a three-qubit XXZ model with Dzyaloshinskii—Moriya (DM) interaction. We find that the effects of DM interaction on antiferromagnetic system is distinct from that of ferromagnetic system. The magnetic field supplemented with DM term contribute to enhance the range of quantum discord. It is revealed that the situations where quantum discord fails to indicate a sudden change of groundstate at finite temperature though indicating such a sudden change of groundstate at zero temperature. Dynamics of pairwise thermal quantum discord is considered as well. Thermal quantum discord vanishes in asymptotic limit regardless of its initial values, however, thermal entanglement suddenly disappears in finite time.
We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic XY\mathrm{XY}XY spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the XY\mathrm{XY}XY model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.