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Property of Many-Body Localization in Heisenberg Ising Chain Under Periodic Driving

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Abstract

We study the property of the many-body localization in Heisenberg Ising Chain model with periodic driving by using the method of matrix exact diagonalization. We consider a driving protocol in which the system’s Hamiltonian is periodically switched between two operators. The first segment is a disordered Ising system, and acts for time T0; It is worth noting that the Hamiltonian of the second part is an operator dependent on time, and acts for time T1, so the driving period is T = T0 + T1. We choose excited state fidelity to observe the phase transition between the localized phase and the ergodic phase of the system, which reflects the property of many-body localization in Heisenberg Ising Chains under periodic driving. Through the study, we find that when the disorder strength h is small, the system is in the ergodic phase, periodic driving can cause the occurrence of a transition from the ergodic phase to the localized phase, while the system is in the localized phase with a large disorder strength h, the transition from the localized phase to the ergodic phase will occur under the periodic driving. For these two cases, they all show that there is a critical driving period Tc, when the driving period is greater than Tc, the system will have a phase transition, meanwhile, Tc decreases with the increase of driving strength. Furthermore, we also get that the system size and disorder strength also effect the critical point of the driving period. The critical point decreases as the strength of disorder increases and decreases with the increase of the system size.

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Data Availability

The datasets generated during and analyzed during the current study are available from the corresponding author on reasonable request.

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Acknowledgments

This work was supported by the NSF of China (Grant No. 62175233) and by the Plan for Scientific and Technological Development of Jilin Province (No. 20220101111JC).

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Authors and Affiliations

  1. School of Physics, Northeast Normal University, Changchun, 130024, People’s Republic of China

    Shuangyuan Ni, Taotao Hu, Kang Xue, Jiali Zhang, Shuang Lu & Xiaoxuan Gu

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

    Hang Ren

  3. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, People’s Republic of China

    Xiaodan Li

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  1. Shuangyuan Ni
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  2. Taotao Hu
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Correspondence to Taotao Hu.

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Ni, S., Hu, T., Ren, H. et al. Property of Many-Body Localization in Heisenberg Ising Chain Under Periodic Driving. Int J Theor Phys 62, 56 (2023). https://doi.org/10.1007/s10773-023-05309-9

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