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When a group of compactly packed free fermions is allowed to spread over anempty one-dimensional lattice, the spreading particles can create entanglementbetween different parts of the lattice. We show, though breaking oftranslational invariance (TI) of the lattice by disorder slows down thespreading of local observables, the entanglement entropy of a subsystem cannonetheless receive a remarkable enhancement as long as the subsystem lieswithin the single-particle localization length. We show, the main mechanismbehind this enhancement is the re-entrant exchange of particles between thesubparts due to transport of mutual information due to back scattering. Wediscuss the length and time scales relevant to the phenomenon. We study thephenomenon for breaking of TI by both quasi-periodic and random potentials. Wefurther explore the effect of randomness only in the initial state. This alsoexhibits a similar enhancement effect even in a TI lattice. We also touch uponthe special case of periodic potential, where qualitatively similarphenomenology emerges, though the coherence in the back scattering in this caseleads to effects not captured by our simple yet generic picture.

Disorder-induced Enhancement of Entanglement Growth in One Dimension: Information Leakage at the scale of localization length