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

TL;DR

This paper investigates how disorder in one-dimensional free fermion systems can enhance entanglement growth within the localization length, despite slowing local observable spreading, due to particle exchange and information transport mechanisms.

Contribution

It reveals the counterintuitive phenomenon of disorder-induced entanglement enhancement within the localization length, analyzing mechanisms and effects of different types of disorder and initial states.

Findings

Entanglement entropy can be enhanced by disorder within the localization length.

Back scattering and mutual information transport drive the entanglement increase.

Similar effects occur with initial state randomness and in periodic potentials.

Abstract

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.