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Negativity and Quantum Phase Transition in the Spin Model Using the Quantum Renormalization-group Method

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Abstract

In this paper, we study the anisotropy parameter and Dzyaloshinskii-Moriya (DM) interaction on negativity and quantum phase transition (QPT) by using the quantum renormalization-group (QRG) method in the spin model. In our model, the anisotropy parameter and DM interaction can influence the phase diagrams. Negativity can develop two different values which separated two phases i.e. Spin-fluid phase and the Néel phase with the number of QRG iterations increased, and can obviously exhibit QPT at the critical point. Then, we find that negativity of particles 1, 3 throughout is less than negativity of particles 1, 2 or particles 2, 3. Because of information between the three particle distributions, please see the conclusion. We find that the negativity difference value (S) can also clearly detect QPT at the critical point. Most importantly, the maximum S max become more and more close to the critical point. So S max can be used as a criterion of the quantum phase transition occurrence when the spin chain is infinity (N → ∞).

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Acknowledgments

This work was supported by the National Science Foundation of China under Grant Nos. 61275119 and 11575001, and also by the Natural Science Research Project of Education Department of Anhui Province of China (Grant No. KJ2013A205).

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Authors and Affiliations

  1. School of Physics & Material Science, Anhui University, Hefei, 230601, China

    Wen-Yang Sun, Shuai Xu, Cheng-Cheng Liu & Liu Ye

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  1. Wen-Yang Sun
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  2. Shuai Xu
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Correspondence to Liu Ye.

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Sun, WY., Xu, S., Liu, CC. et al. Negativity and Quantum Phase Transition in the Spin Model Using the Quantum Renormalization-group Method. Int J Theor Phys 55, 2548–2557 (2016). https://doi.org/10.1007/s10773-015-2890-x

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