Stark Many-Body Localization in Interacting Infinite Dimensional Systems.

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.