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

TL;DR

This paper investigates how relaxation times at different length scales behave in many-body localized systems, revealing that local relaxation is faster than global response due to nonresonant regions affecting transport.

Contribution

It introduces a detailed analysis of length-scale-dependent relaxation in disordered chains and proposes a toy model highlighting the role of nonresonant regions in many-body localization.

Findings

Relaxation time decreases faster at smaller length scales with increasing disorder.

Nonresonant regions cause long relaxation times and can remain frozen.

Nonresonant regions are crucial for understanding global transport in many-body localized systems.

Abstract

We study dynamical correlation functions in the random-field Heisenberg chain, which probes 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 have particularly long relaxation times or remain 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 the disordered chains with many-body interactions.