  The random-field spin-1/2 XXZ chains, and the corresponding Anderson
insulators of spinless fermions with density-density interaction, have been
intensively studied in the context of many-body localization. However, we
recently argued [B. Krajewski et al., Phys. Rev. Lett. 129, 260601(2022)] that
the two-body density-density interaction in these models is not generic since
only a small fraction of this interaction represents a true local perturbation
to the Anderson insulator. Here we study ergodicity of strongly disordered
Anderson insulator chains choosing other forms of the two-body interaction for
which the strength of the true perturbation is of the same order of magnitude
as the bare two-body interaction. Focusing on the strong interaction regime,
numerical results for the level statistics and the eigenstate thermalization
hypothesis are consistent with emergence of ergodicity at arbitrary strong
disorder.
