  Many-body localization (MBL) is an example of a dynamical phase of matter
that avoids thermalization. While the MBL phase is robust to weak local
perturbations, the fate of an MBL system coupled to a thermalizing quantum
system that represents a "heat bath" is an open question that is actively
investigated theoretically and experimentally. In this work we consider the
stability of an Anderson insulator with a finite density of particles
interacting with a single mobile impurity -- a small quantum bath. We give
perturbative arguments that support the stability of localization in the strong
interaction regime. Large scale tensor network simulations of dynamics are
employed to corroborate the presence of the localized phase and give
quantitative predictions in the thermodynamic limit. We develop a
phenomenological description of the dynamics in the strong interaction regime,
and demonstrate that the impurity effectively turns the Anderson insulator into
an MBL phase, giving rise to non-trivial entanglement dynamics well captured by
our phenomenology.
