Entanglement in a dephasing model and many-body localization

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.