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

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.