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The monogamy relation and quantum phase transition in one-dimensional anisotropic XXZ model

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Abstract

In the paper, we have researched the monogamy relation and the quantum phase transition (QPT) in the anisotropic spin XXZ model by exploiting the quantum renormalization group method. The results show that there exits QPT after several iterations of renormalization in the present system. And we can find out that the monogamy inequality of entanglement of formation (EOF) and entropy quantum discord develop two saturated values which associate with spin-liquid and Néel phases after several iterations of the renormalization. Furthermore, we can also find out that the renormalization of EOF and entropy quantum discord violate the monogamy property while the renormalized geometric quantum discord obeys it no matter whether the QPT iterations are carried out. As a byproduct, the nonanalytic phenomenon and scaling behavior of the spin system are analyzed in detail.

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Acknowledgments

This work was supported by the National Science Foundation of China under Grants No. 11074002 and No. 61275119, the Doctoral Foundation of the Ministry of Education of China under Grant No. 20103401110003, the Natural Science Research Project of Education Department of Anhui Province of China under Grant No. KJ2013A205, and also by the Personal Development Foundation of Anhui Province (2008Z018).

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Authors and Affiliations

  1. School of Physics and Material Science, Anhui University, Hefei, 230039, China

    Xue-ke Song, Tao Wu & Liu Ye

  2. School of Physics and Electronics Science, Fuyang Normal College, Fuyang, 236037, China

    Tao Wu

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  1. Xue-ke Song
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  2. Tao Wu
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  3. Liu Ye
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Correspondence to Tao Wu or Liu Ye.

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Song, Xk., Wu, T. & Ye, L. The monogamy relation and quantum phase transition in one-dimensional anisotropic XXZ model. Quantum Inf Process 12, 3305–3317 (2013). https://doi.org/10.1007/s11128-013-0598-5

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  • DOI: https://doi.org/10.1007/s11128-013-0598-5

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