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Chinese Physics B

Thermal quantum discord in Heisenberg models with Dzyaloshinski—Moriya interaction

Lincheng Wang, Jun-Yan Yan, Yi Xue-Xi

Published Apr 1, 2011• 15 citations
Publisher

Abstract

We study the quantum discord of the bipartite Heisenberg model with the Dzyaloshinski-Moriya (DM) interaction in thermal equilibrium state and discuss the effect of the DM interaction on the quantum discord. The quantum entanglement of the system is also discussed and compared with quantum discord. Our results show that the quantum discord may reveal more properties of the system than quantum entanglement and the DM interaction may play an important role in the Heisenberg model.

DOI
10.1088/1674-1056/20/4/040305

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We study the quantum discord of the bipartite Heisenberg model with the Dzyaloshinski-Moriya (DM) interaction in thermal equilibrium state and discuss the effect of the DM interaction on the quantum discord. The quantum entanglement of the system is also discussed and compared with quantum discord. Our results show that the quantum discord may reveal more properties of the system than quantum entanglement and the DM interaction may play an important role in the Heisenberg 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.
Various thermal correlations as well as the effect of intrinsic decoherence on the correlations are studied in a two-qubit Heisenberg XYZ spin chain with the Dzyaloshinski—Moriya (DM) interaction along the z direction, i.e. D z . It is found that tunable parameter D z may play a constructive role on the concurrence C, classical correlation (CC) and quantum discord (QD) in thermal equilibrium while it plays a destructive role on the correlations in the intrinsic decoherence case. The entanglement and quantum discord exhibit collapse and revival under the phase decoherence. With a proper combination of the system parameters, the correlations can effectively be kept at high steady state values despite the intrinsic decoherence.
We investigate the properties of thermal quantum correlations in an infinite spin-1/2 Ising–Heisenberg diamond chain with Dzyaloshinskii–Moriya (DM) interaction. The thermal quantum discord (TQD) and the thermal entanglement (TE) are discussed as two kinds of important methods to measure the quantum correlation, respectively. It is found that DM interaction plays an important role in the thermal quantum correlations of the system. It can enhance the thermal quantum correlations by increasing DM interaction. Furthermore, the thermal quantum correlations can be promoted by tuning the external magnetic field and the Heisenberg coupling parameter in the antiferromagnetic system. It is shown that the behaviors of TQD differ from those of TE. TQD is more robust against decoherence than TE. For the measurement of TQD, the "regrowth" phenomenon occurs in the ferromagnetic system. We also find that the anisotropy favors the thermal quantum correlations of the system with weak DM interaction.
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.
In this paper, we address the tripartite quantum discord for the Heisenberg XY chain with the Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group (QRG) method. In thermodynamic limit, like the entanglement, the tripartite discord exhibits the quantum phase transition (QPT) between the spin-fluid and the Neel phases. The effect of the DM interaction and the anisotropy on the features of the tripartite quantum discord has been probed. It is noted that the DM interaction brings the critical point earlier and affects heavily with the size of the system. Moreover, the system requires a larger number of the iterations to achieve the QPT for the tripartite quantum discord as compared to the entanglement.