Unlimited growth of particle fluctuations in many-body localized phases

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 many-body localization we have recently argued that – contrary established picture particles do not become fully localized. Here summarize and expand on our previous results for various entanglement measures such as number Hartley entropy. investigate, particular, possible alternative interpretations numerical data. find none these appear hold and, process, discover further evidence absence localization. Furthermore, obtain more insights into particle fluctuations by comparing non-interacting systems where derive several strict bounds. renormalized versions bounds also interacting case they provide support numerically discovered scaling relations between entropies.