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Unveiling \({\pi }\)-tangle and quantum phase transition in the one-dimensional anisotropic XY model

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Abstract

In this paper, the relationship between \({\pi }\)-tangle and quantum phase transition (QPT) is investigated by employing the quantum renormalization-group method in the one-dimensional anisotropic XY model. The results show that all the 1-tangles increase firstly and then decrease with the anisotropy parameter \(\gamma \) increasing, and the Coffman–Kundu–Wootters monogamy inequality is always tenable for this system. The entanglement’s status of subsystems depends on its site position, and this proposition can be generalized to a multipartite system. Meanwhile, with the increasing of the size of the system, the \({\pi }\)-tangle decreases slowly and tends to a fixed value finally. Additionally, it exhibits a QPT and a maximum value for the next-nearest-neighbor entanglement at the critical point in our model, which is different from the case of two-body system. After several iterations of the renormalization, the quantum entanglement measure can develop two saturated values, which are associated with two different phases: spin-fluid phase and the Néel phase. To gain further insight, the nonanalytic and scaling behaviors of \({\pi }\)-tangle have also been analyzed in detail.

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Acknowledgments

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

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

    Cheng-Cheng Liu, Shuai Xu, Juan He & Liu Ye

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  1. Cheng-Cheng Liu
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Correspondence to Liu Ye.

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Liu, CC., Xu, S., He, J. et al. Unveiling \({\pi }\)-tangle and quantum phase transition in the one-dimensional anisotropic XY model. Quantum Inf Process 14, 2013–2024 (2015). https://doi.org/10.1007/s11128-015-0982-4

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