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Ground-state and thermal entanglements in non-Hermitian XY system with real and imaginary magnetic fields

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In this manuscript, we study the non-Hermitian spin-1/2 XY model in the presence of the alternating, imaginary and transverse magnetic fields. For the two-site spin system, we solve exactly the energy spectrum and phase diagram and also calculate the ground-state and thermal entanglements by using the concept of the concurrence. It is found that the two-site concurrence in the eigenstate which only depends on the imaginary magnetic field \(\eta \) is always equal to one in the region of \(\mathcal{P}\mathcal{T}\) symmetry, while it decreases with \(\eta \) in the \(\mathcal{P}\mathcal{T}\)-symmetric broken region; especially, the first derivative of concurrence shows the non-analytic behavior at the exceptional point, and the same is true in the case of the biorthogonal basis, which indicates that the concurrence can characterize the phase transition in this non-Hermitian system. The interesting thing is that \(\eta \) weakens the thermal entanglement when the system is isotropic and enhances the entanglement when the system belongs to the Ising universality class. For the one-dimensional spin chain, the magnetization and entanglement are further studied by using the two-spin cluster mean-field approximation. The results show that their variations have opposite trends with the magnetic fields. Moreover, the system exists the first-order quantum phase transitions for some anisotropic parameters in the \(\mathcal{P}\mathcal{T}\)-symmetry region, and the entanglement changes suddenly at the quantum phase transition point.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China under Grants Nos. 11675090 and 11905095; Shandong Provincial Natural Science Foundation, China, under Grant No. ZR202111160185. Y. Li. would like to thank Chun-Yang Wang, Jing Wang, Zhen-Hui Sun, Xiu-Ying Zhang, Qing-Hui Li, and Chuan-Zheng Miao for fruitful discussions and useful comments.

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  1. School of Physics and Optoelectronic Engineering, Institute of Theoretical Physics, Ludong University, Yantai, 264025, China

    Yue Li, Pan-Pan Zhang, Li-Zhen Hu, Yu-Liang Xu & Xiang-Mu Kong

  2. Department of Physics, Beijing Normal University, Beijing, 100875, China

    Pan-Pan Zhang & Li-Zhen Hu

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  1. Yue Li
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Li, Y., Zhang, PP., Hu, LZ. et al. Ground-state and thermal entanglements in non-Hermitian XY system with real and imaginary magnetic fields. Quantum Inf Process 22, 277 (2023). https://doi.org/10.1007/s11128-023-04031-z

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