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arXiv:1002.0176

Thermal quantum discord in the anisotropic Heisenberg XXZ model with the Dzyaloshinskii-Moriya interaction

Yi-Xin Chenand, Zhi Yin

Published Feb 1, 2010• 2 citations
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Abstract

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 $T$ while entanglement decreases to zero at the point of critical temperature, situations where QD decreases with certain tunable parameters such as $D_z$ and $D_x$ 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 $D_x$ is more efficient than parameter $D_z$ in most regions for controlling the QD.

DOI
10.48550/arxiv.1002.0176

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The thermal quantum discord (QD) is studied in a two-qubit Heisenberg XXZ system with Dzyaloshinskü–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 T while entanglement decreases to zero at the point of critical temperature, situations where QD decreases with certain tunable parameters such as D z and D x 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 D x is more efficient than parameter D z in most regions for controlling the QD.
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.
The thermal entanglement is investigated in a two-qubit Heisenberg XXZ system with Dzyaloshinskii–Moriya (DM) interaction. It is shown that the entanglement can be efficiently controlled by the DM interaction parameter and coupling coefficient J z . D x (the x -component parameter of the DM interaction) has a more remarkable influence on the entanglement and the critical temperature than D z (the z -component parameter of the DM interaction). Thus, by changing the DM interaction direction, we can get a more efficient control parameter to increase the entanglement and the critical temperature.
The thermal quantum discord (QD) is investigated in the two-qubit anisotropic Heisenberg XXZ model under an external non-uniform magnetic field along the Z-axis. We obtain the analytical expressions of the thermal QD and thermal entanglement measured by concurrence (C). It shows that for any temperature T, QD gradually decreases with the increase of non-uniform magnetic field |b|, in some regions where C increases while QD decreases. It is also found that thermal quantum discord does not vanish at finite temperatures, but concurrence vanishes completely at a critical temperature. It is shown that for a higher value of JZ, the system has a stronger QD. There is a critical magnetic field B c , which increases with the increasing b. QD decay monotonically (for B < B c ) when temperature T increases, or initially increases to some peaks and then decrease (for B > B c ).
We have investigated the quantum discord (QD) of the thermal density matrix of spin-1/2 Heisenberg chains with Dzyaloshinskii–Moriya (DM) interaction. With fermionization technique, we study the mutual effect of DM interaction and the external magnetic field on the QD and the entanglement. Our analysis implies that the DM interaction can enhance the QD while the external magnetic field will shrink the QD. By a comparison between the entanglement and the QD, we find that the QD is more robust to the temperature and to the external magnetic field than the entanglement of formation (EoF) in the sense that the EoF takes a zero value while the QD does not for high temperature and strong external magnetic field. This point confirms the conclusion that there exist some separable states containing non-zero QD.