Relaxation at different length-scales in models of many-body localization

J. Herbrych,1 M. Mierzejewski,1 P. Prelovšek2,3

1Wrocław University of Science and Technology, 50-370 Wrocław, Poland

2Jožef Stefan Institute, SI-1000 Ljubljana, Slovenia

3University of Ljubljana, SI-1000 Ljubljana, Slovenia

We study dynamical correlation functions in the random-field Heisenberg chain, which probe the relaxation times at different length scales. Firstly, we show that the relaxation time associated with the dynamical imbalance (examining the relaxation at the smallest length scale) decreases with disorder much faster than the one determined by the dc conductivity (probing the global response of the system). We argue that the observed dependence of relaxation on the length scale originates from local nonresonant regions. The latter has particularly long relaxation times or remains frozen, allowing for nonzero dc transport via higher-order processes. Based on the numerical evidence, we introduce a toy model that suggests that the nonresonant regions‘ asymptotic dynamics are essential for the proper understanding of disordered chains. In addition, the toy model explains the exponential dependence of the transport properties on the disorder and the broad distribution of dc conductivity.

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