Evidence for unbounded growth of the number entropy in many-body localized phases

TL;DR

This paper provides evidence that in many-body localized phases, the number entropy grows unboundedly as a double logarithm of time, suggesting ongoing particle transport despite localization.

Contribution

The study reveals that number entropy in MBL phases grows as ln(ln t), indicating slow but persistent particle transport, extending understanding of entanglement dynamics in disordered systems.

Findings

Number entropy grows as ln(ln t) in MBL phases.

Evidence of ongoing particle transport in localized regimes.

Growth pattern aligns with relations established in non-interacting systems.

Abstract

We investigate the number entropy $S_N$---which characterizes particle-number fluctuations between subsystems---following a quench in one-dimensional interacting many-body systems with potential disorder. We find evidence that in the regime which is expected to show many-body localization (MBL) and where the entanglement entropy grows as $S\sim \ln t$ as function of time $t$, the number entropy grows as $S_N\sim\ln\ln t$, indicating continuing particle transport at a very slow rate. We demonstrate that this growth is consistent with a relation between entanglement and number entropy recently established for non-interacting systems.