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Chinese Physics B

Monogamy of quantum correlations in the one-dimensional anisotropic XY model

Shuai Xu, Xue‐Ke Song, Liu Ye

Published Jan 1, 2014• 3 citations
Publisher

Abstract

In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii—Moriya (DM) interaction have been investigated using the quantum renormalization group (QRG) method. We summarize the monogamy relation for different quantum correlation measures and make an explicit comparison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.

DOI
10.1088/1674-1056/23/1/010302

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In this paper, the monogamy properties of some quantum correlations, including the geometric quantum discord, concurrence, entanglement of formation and entropy quantum discord, in the anisotropic spin-1/2 XY model with staggered Dzyaloshinskii—Moriya (DM) interaction have been investigated using the quantum renormalization group (QRG) method. We summarize the monogamy relation for different quantum correlation measures and make an explicit comparison. Through mathematical calculations and analysis, we obtain that no matter whether the QRG steps are carried out, the monogamy of the given states are always unaltered. Moreover, we conclude that the geometric quantum discord and concurrence obey the monogamy property while other quantum correlation measures, such as entanglement of formation and quantum discord, violate it for this given model.
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.
The purpose of the paper is mainly to investigate the quantum critical behavior of two-dimensional XY spin system by calculating quantum correlation and monogamy relation through implementation of quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can be used to efficiently detect the quantum critical property in two-dimensional XY spin system. The nonanalytic behavior of the first derivative of quantum correlation approaches infinity and the critical point is reached as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this model based on square of concurrence (SC) and square of quantum discord (SQD). The monogamous properties of SC and SQD are obtained for the present system. We finally reveal that the monogamy score can be used to capture the quantum critical point.
\n\nIn order to define quantum correlations, there are two important paradigms in quantum information theory, viz. the information-theoretic and the entanglement-separability ones. In this paper, we give an analytical relation between two measures of quantum correlations. One of them is related to the monogamy of squared bipartite quantum discord, which is a information-theoretic multipartite quantum correlation measure, while the other is the generalized geometric measure which lies in the entanglement-separability paradigm. We find a certain cone-like region on the two-dimensional spaces spanned by the two measures. Moreover, we have investigated the quantum phase transition with the two measures in the anisotropic spin XXZ model by exploiting the quantum renormalization group method.\n
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.
The purpose of the paper is mainly to investigate the quantum critical behavior of two-dimensional XY spin system by calculating quantum correlation and monogamy relation through implementation of quantum renormalization group theory. Numerical analysis indicates that quantum correlation as well as quantum nonlocality can be used to efficiently detect the quantum critical property in two-dimensional XY spin system. The nonanalytic behavior of the first derivative of quantum correlation approaches infinity and the critical point is reached as the size of the model increases. Furthermore, we discuss the quantum correlation distribution in this model based on square of concurrence (SC) and square of quantum discord (SQD). The monogamous properties of SC and SQD are obtained for the present system. We finally reveal that the monogamy score can be used to capture the quantum critical point.