Entanglement in a dephasing model and many-body localization

TL;DR

This paper investigates entanglement growth in a many-body localized system modeled by an l-bit dephasing framework, revealing a sublogarithmic correction to the expected logarithmic growth.

Contribution

It provides an exact expression for entanglement dynamics in the l-bit model, challenging the previous belief that entanglement grows solely logarithmically in MBL phases.

Findings

Entanglement growth includes a sublogarithmic correction.

Exact analytical expression for entanglement dynamics is derived.

Results suggest entanglement growth is slower than previously thought.

Abstract

We study entanglement dynamics in a diagonal dephasing model in which the strength of interaction decays exponentially with distance -- the so-called l-bit model of many-body localization. We calculate the exact expression for entanglement growth with time, finding in addition to a logarithmic growth, a sublogarithmic correction. Provided the l-bit picture correctly describes the many-body localized phase this implies that the entanglement in such systems does not grow (just) as a logarithm of time, as believed so far.