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International Journal of Quantum Information

Quantum discord in spin-1/2 Heisenberg chains with Dzyaloshinkii–Moriya interaction

XIAO SAN MA, An Min Wang

Published Dec 10, 2014• 1 citation
Publisher

Abstract

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.

DOI
10.1142/s0219749914500439

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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.
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.
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 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 the present work, we first verify pairwise quantum discord (QD) between half-spins of a mixed three-spin (1/2,1,1/2) system with Ising-XY model for which spins (1,1/2) have Ising interaction and spins (1/2,1/2) have both XY and Dzyaloshinskii-Moriya (DM) interactions. A single-ion anisotropy property ζ is assumed for integer spin. This system is considered at the front of an external homogeneous magnetic field B in thermal equilibrium. Then, we investigate the pairwise entanglement between half-spins by using entanglement of formation (EoF) as functions of temperature T , magnetic field B and other introduced parameters. In this case, all parameters are independent of the temperature. We compare the QD and the EoF verified for the spins (1/2,1/2) and express some interesting temperature, magnetic and quantum correlation properties. Also, we study the anisotropy influences on the quantum correlation between such spins in detail, and we find that this parameter can be used as a quantum discord controller. In the second step, we investigate QD for the half-spins in a stochastic manner, i.e. , when all parameters of the tripartite system are constant (independent of the temperature) except the anisotropy, which is considered as a random variable dependent on the temperature. Finally, we assume that all parameters are constant except the Ising coupling strength, which can change randomly with temperature. Ultimately, we conclude that in the experimental conditions under which some parameters may have stochastic behavior, the anisotropy can also be a good candidate to control QD.