Abstract

There is a growing consensus that generic disordered quantum wires, e.g. the XXZ-Heisenberg chain, do not exhibit many-body localization (MBL) - at least not in a strict sense within a reasonable window of disorder values. Specifically, computational studies of short wires exhibit an extremely slow but unmistakable flow of physical observables with increasing time and system size (`creep') that is consistently directed away from (strict) localization. Our work sheds fresh light on delocalization physics: Strong sample-to-sample fluctuations indicate the absence of a generic time scale, i.e., of a naive "clock rate"; however, the concept of an "internal clock" survives, at least in an ensemble sense.
Specifically, we investigate the relaxation of the charge imbalance and the entanglement entropy in a 1D system of interacting disordered fermions. We observe that the average entropy appropriately models the ensemble-averaged internal clock and reduces fluctuations. We take the tendency for faster-than-logarithmic growth of entanglement and smooth dependency on the disorder of all our observables within the entire simulation window as support for the cross-over scenario, discouraging an MBL transition within the traditional parametric window of computational studies.