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International Journal of Quantum Information

Quantum correlations in Heisenberg XY spin-1 and spin-1/2 model with Dzyaloshinskii–Moriya interactions

Wajid Joyia

Published Aug 1, 2015• 5 citations
Publisher

Abstract

We study the quantum correlations in a spin-1/2 (qubit) and spin-1 (qutrit) Heisenberg XY model separately, based on quantum discord (QD) and measurement-induced disturbance (MID) respectively. We find the evidence of the first- and second-order quantum phase transition (QPT) in both spin-1/2 and spin-1 systems. The effect of the temperature, magnetic field and Dzyaloshinskii–Moriya (DM) interactions on QPT and quantum correlation are also investigated. Finally, we observed that the QD and MID are not only vigorous for higher spin systems but also more robust than entanglement.

DOI
10.1142/s0219749915500355

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We study the quantum correlations in a spin-1/2 (qubit) and spin-1 (qutrit) Heisenberg XY model separately, based on quantum discord (QD) and measurement-induced disturbance (MID) respectively. We find the evidence of the first- and second-order quantum phase transition (QPT) in both spin-1/2 and spin-1 systems. The effect of the temperature, magnetic field and Dzyaloshinskii–Moriya (DM) interactions on QPT and quantum correlation are also investigated. Finally, we observed that the QD and MID are not only vigorous for higher spin systems but also more robust than entanglement.
We study the dynamics of correlations for a hybrid qubit—qutrit system in an XY spin-chain environment with Dzyaloshinsky—Moriya interaction. Our discussion involves a comparative analysis of negativity, quantum discord, and measurement-induced disturbance. It is found that the quantum discord is optimal of the three quantum correlations to detect the critical point of quantum phase transition. Only when the qubit interacts with the environment, is the phenomenon of sudden transition between the classical correlation and the quantum discord observed. Moreover, the Dzyaloshinsky—Moriya interaction enhances the decay of quantum correlations.
Quantum correlations measured by quantum discord (QD), measurement-induced distance (MID), and geometric measure of quantum discord (GMQD) in two-qubit Heisenberg XY spin chain are investigated. The effects of DM interaction and anisotropic on the three correlations are considered. Characteristics of various correlation measures for the two-qubit states are compared. The increasing D z increases QD, MID and GMQD monotonously while the increasing anisotropy both increases and decreases QD and GMQD. The three quantum correlations are always existent at very high temperature. MID is always larger than QD, but there is no definite ordering between QD and GMQD.
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.
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 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.
We examine the ability of quantum discord (QD) and entanglements (concurrence, EoF and negativity) to detect the critical points associated to quantum phase transitions (QPTs) for XY models, i.e., the isotropic XY model with three-spin interactions at zero temperature, and the anisotropic XY model in a transverse magnetic field h at finite temperatures. For the case of zero temperature, we found that both entanglements and QD can spotlight the critical points of QPTs for these two models. Moreover, QD versus distance M exhibits the long-range behavior of quantum correlation for the anisotropic XY model, while entanglement is short-ranged. For the case of finite temperatures, we found that negativity has the same behaviors with concurrence at or near transition points. Moreover, QD for the anisotropic XY model can increase with temperature even in the absence of a magnetic field.