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arXiv:1012.2788 · Physical Review A

Quantum and classical correlations in the one-dimensional XY model with Dzyaloshinskii-Moriya interaction

Ben‐Qiong Liu, Bin Shao, Jungang Li, Jian Zou, Lian-Ao Wu

Published May 12, 2011• 120 citations
arXivHTMLPDF

Abstract

We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic $\mathrm{XY}$ spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the $\mathrm{XY}$ model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.

DOI
10.1103/physreva.83.052112

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We study the effect of Dzyaloshinskii-Moriya (DM) interaction on pairwise quantum discord, entanglement, and classical correlation in the anisotropic XY\mathrm{XY}XY spin-half chain. Analytical expressions for both quantum and classical correlations are obtained from the spin-spin correlation functions. These pairwise quantities exhibit interesting behaviors in relation to the relative strengths of the physical parameters. For the infinite chain, we show that the quantum discord can be useful to highlight the quantum phase transition, especially for the long-distance spins, where entanglement decays rapidly. We observe nonanalyticities of the derivatives of both quantum and classical correlations with respect to the magnetic intensity at the critical point; interestingly, the DM interaction weakens the critical behavior in the derivatives of these correlations. While the DM interaction suppresses the standard behaviors of the XY\mathrm{XY}XY model, it enhances surprisingly the pairwise entanglement for the third nearest neighbor spins.
We study the dynamics of quantum discord and entanglement for two spin qubits coupled to a spin chain with Dzyaloshinsky-Moriya (DM) interaction. We numerically and analytically investigate the time evolution of quantum discord and entanglement for two-qubit initially prepared in a class of X−X-X−structure state. In the case of evolution from a pure state, quantum correlations decay to zero in a very short time at the critical point of the environment. In the case of evolution from a mixed state, It is found that quantum discord may get maximized due to the quantum critical behavior of the environment while entanglement vanishes under the same condition. Moreover, we observed sudden transition between classical and quantum decoherence when single qubit interacts with the environment. The effects of DM interaction on quantum correlations are also considered and revealed in the two cases. It can enhance the decay of quantum correlations and its effect on quantum correlations can be strengthened by anisotropy parameter.
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 study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.
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.
In the present work, initially, a mixed-three-spin (1/2,1,1/2) cell of a mixed-[Formula: see text]-spin chain with Ising-XY model is introduced, for which pair spins (1,1/2) have Ising-type interaction and pair spins (1/2,1/2) have both XY-type and Dzyaloshinskii–Moriya (DM) interactions together. An external homogeneous magnetic field [Formula: see text] is considered for the system in thermal equilibrium. Integer-spins have a single-ion anisotropy property with coefficient [Formula: see text]. Then, we investigate the quantum entanglement between half-spins (1/2,1/2), by means of the concurrence. Classical correlation (CC) for this pair of spins is investigated as well as the concurrence and some interesting temperature, the magnetic field and the DM interaction properties are expressed. Moreover, single-ion anisotropy effects on the correlation between half-spins is verified. According to the verifications based on the communication channels category by Rossini, Giovannetti and Fazio [D. Rossini, V. Giovannetti and R. Fazio, Int. J. Quantum Inf. 5, 439 (2007)], we theoretically consider such tripartite spin model as an ideal quantum channel, then calculate its information transmission rate and express some differences in behavior between this suggested model and introduced simple models in the previous works (chains without spin integer and DM interaction) from information transferring protocol point of view.
In this paper, we use the negativity and geometric quantum discord (GQD) to investigate the quantum phase transition (QPT) in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii–Moriya (DM) interaction using the quantum renormalization-group method, and the results show that the negativity and GQD can both obtain the quantum critical points associated with QPTs after several iterations of the renormalization. In addition to this, we discuss how the strength of the DM interaction and anisotropic parameter make the effect on the negativity and GQD for different RG steps. At last, we give out the relationship between negativity and GQD, and verify that with anisotropy parameter and the strength of DM interaction increased, the squared negativity and the normalization of GQD tend to equal in this model.