Absence of true localization in many-body localized phases

@article{KieferEmmanouilidis2020AbsenceOT,
  title={Absence of true localization in many-body localized phases},
  author={Maximilian Kiefer-Emmanouilidis and Razmik G. Unanyan and Michael Fleischhauer and Jesko Sirker},
  journal={arXiv: Disordered Systems and Neural Networks},
  year={2020}
}
We have recently shown that the logarithmic growth of the entanglement entropy following a quantum quench in a many-body localized (MBL) phase is accompanied by a slow growth of the number entropy, $S_N\sim\ln\ln t$. This violates the standard scenario of MBL and raises the question whether the observed behavior is transient or continues to hold at strong disorder in the thermodynamic limit. Here we provide an in-depth numerical study of $S_N(t)$ for the disordered Heisenberg chain and find… 

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