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Quantum phase transition, quantum fidelity and fidelity susceptibility in the Yang–Baxter system

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Abstract

In this paper, we investigate the ground-state fidelity and fidelity susceptibility in the many-body Yang–Baxter system and analyze their connections with quantum phase transition. The Yang–Baxter system was perturbed by a twist of \( e^{i\varphi } \) at each bond, where the parameter \( \varphi \) originates from the q-deformation of the braiding operator U with \(q = e^{-i\varphi }\) (Jimbo in Yang–Baxter equations in integrable systems, World Scientific, Singapore, 1990), and \( \varphi \) has a physical significance of magnetic flux (Badurek et al. in Phys. Rev. D 14:1177, 1976). We test the ground-state fidelity related by a small parameter variation \(\varphi \) which is a different term from the one used for driving the system toward a quantum phase transition. It shows that ground-state fidelity develops a sharp drop at the transition. The drop gets sharper as system size N increases. It has been verified that a sufficiently small value of \(\varphi \) used has no effect on the location of the critical point, but affects the value of \( F(g_{c},\varphi ) \). The smaller the twist \(\varphi \), the more the value of \( F(g_{c},\varphi ) \) is close to 0. In order to avoid the effect of the finite value of \( \varphi \), we also calculate the fidelity susceptibility. Our results demonstrate that in the Yang–Baxter system, the quantum phase transition can be well characterized by the ground-state fidelity and fidelity susceptibility in a special way.

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Acknowledgements

This work is supported by NSF of China (Grants No. 11305033), the Plan for Scientific and Technological Development of Jilin Province (No. 20160520112JH). T.T.H. was also supported in part by the Government of China through CSC.

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Authors and Affiliations

  1. School of Physics, Northeast Normal University, Changchun, 130024, China

    Taotao Hu, Qi Yang, Kang Xue, Gangcheng Wang & Yan Zhang

  2. Key Laboratory of Airborne Optical Imaging and Measurement, Changchun Institute of Optics, Fine Mechanics and Physics, Chinese Academy of Sciences, Changchun, 130033, China

    Hang Ren

  3. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Xiaodan Li

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  1. Taotao Hu
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Correspondence to Taotao Hu.

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Hu, T., Yang, Q., Xue, K. et al. Quantum phase transition, quantum fidelity and fidelity susceptibility in the Yang–Baxter system. Quantum Inf Process 16, 21 (2017). https://doi.org/10.1007/s11128-016-1487-5

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