Slow delocalization of particles in many-body localized phases - Kiefer-Emmanouilidis, Maximilian; Unanyan, Razmik; Fleischhauer, Michael; Sirker, Jesko (Physical Review B, 2021)
We have recently shown that the logarithmic growth of the entanglement entropy following a quantum quench in a many-body localized phase is accompanied by a slow growth of the number entropy SN∼lnlnt. Here we provide an in-depth numerical study of SN(t) for the disordered Heisenberg chain and show that this behavior is not transient and persists even for very strong disorder. Calculating the truncated Rényi number entropy SN(α)(t)=(1-α)-1ln∑npα(n) for α1 and p(n)>pc - which is sensitive to large number fluctuations occurring with low probability - we demonstrate that the particle number distribution p(n) in one half of the system has a continuously growing tail. This indicates a slow but steady increase in the number of particles crossing between the partitions in the interacting case and is in sharp contrast to Anderson localization for which we show that SN(α→0)(t) saturates for any cutoff pc>0. We show, furthermore, that the growth of SN is not the consequence of rare states or rare regions but rather represents typical behavior. These findings indicate that the interacting system is never fully localized even for very strong but finite disorder.
CRIS-Team Scopus Importer:2023-03-27