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The Behavior of Many-Body Localization of Quasi-Disordered Spin-1/2 Chains

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Abstract

We theoretically study properties of the many-body localization (MBL) in the quasi-disordered one-dimensional spin-1/2 chains at finite temperature. We extend the problem of individual localization of disordered systems to quasi-disordered many-body interaction systems, introducing disorder with a more controllable method to show the uniqueness of quasi-disordered designs. In this paper, the interplay among interaction and quasi-disordered fields is investigated comprehensively by using the exact matrix diagonalization. It is demonstrated that the fidelity of eigenstate is able to characterize the many-body localization transition in closed spin system (Gu, Int. J. Mod. Phys. B 24, 4371–4458, 2010). We compute the fidelity for high-energy many-body eigenstates, which shows the phase transition of one-dimensional spin-1/2 chains. Our results reveal that the quasi-disordered can cause the occurrence of a transition from the ergodic phase to the localized phase, which agrees with Lee’s recent studies (Lee et al., Phys. Rev. B 96, 075146, 2017). Besides, we plot the averaged fidelity as a function of the disorder strength h for system sizes from 8 to 14 with five different coupling coefficient ratios. It also shows that the interplay between disorder and interaction constitutes the driving mechanism of the MBL transition. The more complex the interaction between the two particles, the more difficult it is to lead to many-body delocalization.

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Acknowledgements

This work was supported by the NSF of China (Grant No. 62175233).

Funding

This work was supported by the NSF of China (Grant No. 62175233).

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Authors and Affiliations

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

    Jiali Zhang, Taotao Hu, Kang Xue, Shuangyuan Ni, 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. Jiali Zhang
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Contributions

Taotao H, Jiali Zhang contributed the idea. Taotao Hu, Jiali Zhang, Shuangyuan Ni performed the calculations and prepared the figures. Jiali Zhang wrote the main manuscript. Taotao Hu, Kang Xue, Xiaodan Li, Shuang Lu, Xiaoxuan Gu 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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Zhang, J., Hu, T., Ren, H. et al. The Behavior of Many-Body Localization of Quasi-Disordered Spin-1/2 Chains. Int J Theor Phys 61, 122 (2022). https://doi.org/10.1007/s10773-022-05108-8

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