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arXiv:1207.0277 · Chinese Physics Letters

Various Correlations in the Anisotropic HeisenbergXYZModel with Dzyaloshinski—Moriya Interaction

Mamtimin Tursun, Ahmad Abliz, Rabigul Mamtimin, Ablimit Abliz, Pan-Pan Qiao

Published Mar 1, 2013• 19 citations
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Abstract

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.

DOI
10.1088/0256-307x/30/3/030303

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We investigate the quantum correlations of a two-qubit XYZ Heisenberg spin-1/2 chain model with Dzyaloshinskii–Moriya interaction. The two-qubit system is considered in thermal equilibrium. The variations of logarithmic negativity, uncertainty-induced quantum nonlocality (UIN) and trace distance discord, versus the parameters characterizing the system, are analyzed. The results show that the UIN measure captures quantum correlations that cannot be revealed by entanglement and trace discord. We also show that the Dzyaloshinskii–Moriya interaction enhances the non-classical correlations between the spins and can weaken the undesirable destructive effects of thermal fluctuations. In addition, an entangled–unentangled phase transition can be detected from the behavior of logarithmic negativity.
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.
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.
The quantum correlation dynamics in an anisotropic Heisenberg XYZ model under decoherence are investigated with the use of concurrence C and quantum discord (QD). There is a remarkable difference between the time evolution behaviors of these two correlation measures: there is a entanglement-sudden-death phenomenon in the concurrence while there is none in QD, which is valid for all of the initial states of this system, and the interval time of the entanglement death is found to be strongly dependent on the initial states and the parameters B and Δ. With the long-time limit the steady entanglement (SC) and steady quantum discord (SQD) can be obtained. The magnitudes of SC and SQD are closely related to the parameters B and Δ, while the strength of the Dzyaloshinskii—Moriya interaction, D, has no influence. In addition, the effects of the parameters B and Δ on SC and SQD display such different and complicated features that one cannot obtain a uniform law about them, thus we give an analytical explanation of this phenomenon. Lastly, it can be noted that the value of SC is not always larger than SQD, which is strongly dependent on the parameters B and Δ.