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Renormalization of the global quantum correlation and monogamy relation in the anisotropic Heisenberg XXZ model

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Abstract

In this study, the global quantum correlation, monogamy relation and quantum phase transition of the Heisenberg XXZ model are investigated by the method of quantum renormalization group. We obtain, analytically, the expressions of the global negativity, the global measurement-induced disturbance and the monogamy relation for the system. The result shows that for a three-site block state, the partial transpose of an asymmetric block can get stronger entanglement than that of the symmetric one. The residual entanglement and the difference of the monogamy relation of measurement-induced disturbance show a scaling behavior with the size of the system becoming large. Moreover, the monogamy nature of entanglement measured by negativity exists in the model, while the nonclassical correlation quantified by measurement-induced disturbance violates the monogamy relation and demonstrates polygamy.

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Acknowledgments

This work was supported by the National Natural Science Foundation of China (Grant Nos. 11535004, 11375086, 11105079 and 10975072), by the Research and Innovation Project for College Postgraduate of JiangSu Province (Grant Nos. KYZZ15_0027), by the 973 National Major State Basic Research and Development of China (Grant Nos. 2010CB327803 and 2013CB834400), by CAS Knowledge Innovation project no KJCX2-SW-N02, by Research Fund of Doctoral Point (RFDP) (Grant Nos. 20100091110028), by the Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD) and by the Deutsche Forschungsgemeinschaft through TRR80.

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Authors and Affiliations

  1. Department of Physics and Key Laboratory of Modern Acoustic, Nanjing University, Hankou Road 22, Nanjing, 210093, China

    Meng Qin, Zhong-Zhou Ren & Xin Zhang

  2. College of Sciences, PLA University of Science and Technology, Nanjing, 211101, China

    Meng Qin

  3. Center of Theoretical Nuclear Physics, National Laboratory of Heavy-Ion Accelerator, Lanzhou, 730000, China

    Zhong-Zhou Ren

  4. Kavli Institute for Theoretical Physics, Chinese Academy of Sciences, Beijing, 100190, China

    Zhong-Zhou Ren

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  1. Meng Qin
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Correspondence to Meng Qin.

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Qin, M., Ren, ZZ. & Zhang, X. Renormalization of the global quantum correlation and monogamy relation in the anisotropic Heisenberg XXZ model. Quantum Inf Process 15, 255–267 (2016). https://doi.org/10.1007/s11128-015-1167-x

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  • DOI: https://doi.org/10.1007/s11128-015-1167-x

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