  When a group of compactly packed free fermions is allowed to spread over an
empty one-dimensional lattice, the spreading particles can create entanglement
between different parts of the lattice. We show, though breaking of
translational invariance (TI) of the lattice by disorder slows down the
spreading of local observables, the entanglement entropy of a subsystem can
nonetheless receive a remarkable enhancement as long as the subsystem lies
within the single-particle localization length. We show, the main mechanism
behind this enhancement is the re-entrant exchange of particles between the
subparts due to transport of mutual information due to back scattering. We
discuss the length and time scales relevant to the phenomenon. We study the
phenomenon for breaking of TI by both quasi-periodic and random potentials. We
further explore the effect of randomness only in the initial state. This also
exhibits a similar enhancement effect even in a TI lattice. We also touch upon
the special case of periodic potential, where qualitatively similar
phenomenology emerges, though the coherence in the back scattering in this case
leads to effects not captured by our simple yet generic picture.
