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The Behavior of Many-body Localization in the Periodically Driven Heisenberg XXX Model

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Abstract

In this paper, we use exact matrix diagonalization to research property of the many-body localization (MBL) in the disordered Heisenberg XXX model with periodic driving. We get the periodic time-dependent external field by trigonometric function, which is added to periodically drive this model. It is demonstrated that the fidelity of eigenstate is able to capture quantum criticality underlying many-body physics (Zhou et al. Phys. Rev. Lett. 100, 080601, 2008, Zhou and Barjaktarevi J. Phys. A: Math. Theor. 41, 412001 2008), which can be used to characterize the many-body localization transition in this closed spin system (Zanardi and Paunkovic Phys. Rev. E 74, 031123, 2006). We obtain the fidelity for high-energy many-body eigenstates, namely, the excited state fidelity, which shows the phase transition of periodically driven Heisenberg XXX chain with different disordered external field strengths and different system sizes. It is demonstrated that when Heisenberg XXX system is in a very small disorder, periodic driving can cause the occurrence of a transition from ergodic phase to MBL phase. In contrast to the HS model which has global two-body interaction, which we have studied recently with the same situation, there is no MBL phase transition when we drive the HS model in ergodic phase with periodic driving. It also shows that for the strong disordered Heisenberg XXX system, there will exist a critical driving period Tc, when driving period T is higher than Tc, the system will undergo a transition from localized phase to ergodic phase and the MBL phase will be broken. Furthermore, we discover that the size of the system and the strength of disorder will affect the critical point of driving period and the magnitude of the phase change. For the same system, the critical point increases as the strength of disorder increases. We also explore the non-disorder system of HS model with the same driving to explore the properties of MBL, it shows that under periodic driving, the non-disordered HS system has the quantum phase transition rather than MBL phase transition. This illustrates the important role of disorder on MBL.

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Acknowledgments

This work is supported by “the Fundamental Research Funds for the Central Universities” (No. 2412019FZ037).

Funding

This work is supported by “the Fundamental Research Funds for the Central Universities” (No. 2412019FZ037) and by Special fund of NSF of China (Grant No. 11947405).

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Authors and Affiliations

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

    Hui Zhao, Taotao Hu, Kang Xue, Haoyue Li, Shuangyuan Ni & Jiali Zhang

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

    Xiaodan Li

  3. 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

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  1. Hui Zhao
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Contributions

Taotao H, Hui Zhao contributed the idea. Taotao Hu, Hui Zhao, Haoyue Li performed the calculations and prepared the figures. Hui Zhao wrote the main manuscript. Taotao Hu, Kang Xue, Xiaodan Li, Shuangyuan Ni, Jiali Zhang and Hang Ren checked the calculations and improved the manuscript. All authors contributed to discussions and reviewed the manuscript.

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Correspondence to Taotao Hu.

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Zhao, H., Hu, T., Xue, K. et al. The Behavior of Many-body Localization in the Periodically Driven Heisenberg XXX Model. Int J Theor Phys 60, 3177–3187 (2021). https://doi.org/10.1007/s10773-021-04843-8

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