paper

The internal clock of many-body delocalization

arXiv:2302.11384 · doi:10.1103/PhysRevB.108.134204

Abstract

After a decade of many claims to the opposite, there now 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 imbalance and its temporal fluctuations , the entanglement and Renyi entropies, and , in a 1D system of interacting disordered fermions. We observe that adopting as a measure for the internal time per sample reduces the sample-to-sample fluctuations but does not eliminate them. However, a (nearly) perfect collapse of the average and for different is obtained when plotted against or , indicating that the average entropy appropriately models the ensemble-averaged internal clock. We take the tendency for faster-than-logarithmic growth of together with smooth dependency on 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.

arXiv comment15 pages, 12+5 figures, published version

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