Unlimited growth of particle fluctuations in many-body localized phases

TL;DR

This paper investigates the dynamics of particle fluctuations and entanglement in a disordered many-body system, providing evidence against full localization and revealing scaling relations in the non-equilibrium behavior.

Contribution

It offers new insights into the absence of localization in many-body localized phases and extends previous results with additional entanglement and fluctuation analyses.

Findings

Particles do not fully localize in the studied model.

Entanglement and particle fluctuations follow specific scaling relations.

Bounds from non-interacting systems also apply to the interacting case.

Abstract

We study quench dynamics in a t-V chain of spinless fermions (equivalent to the spin-1/2 Heisenberg chain) with strong potential disorder. For this prototypical model of many-body localization we have recently argued that -- contrary to the established picture -- particles do not become fully localized. Here we summarize and expand on our previous results for various entanglement measures such as the number and the Hartley number entropy. We investigate, in particular, possible alternative interpretations of our numerical data. We find that none of these alternative interpretations appears to hold and, in the process, discover further strong evidence for the absence of localization. Furthermore, we obtain more insights into the entanglement dynamics and the particle fluctuations by comparing with non-interacting systems where we derive several strict bounds. We find that renormalized versions of these bounds also hold in the interacting case where they provide support for numerically discovered scaling relations between number and entanglement entropies.