Diffusive and subdiffusive spin transport in the ergodic phase of a many-body localizable system

TL;DR

This paper investigates high-temperature spin transport in a disordered Heisenberg chain, revealing diffusive and subdiffusive phases, large crossover lengths, and providing insights into steady-state magnetization profiles.

Contribution

It introduces a large-scale DMRG approach to study spin transport, uncovering the existence of a large crossover length and characterizing diffusive and subdiffusive regimes in disordered systems.

Findings

Identification of diffusive and subdiffusive phases depending on disorder and anisotropy.

Discovery of a large crossover length affecting the observed dynamics.

Prediction of magnetization profiles in non-diffusive steady states.

Abstract

We study high temperature spin transport in a disordered Heisenberg chain in the ergodic regime. By employing a density matrix renormalization group technique for the study of the stationary states of the boundary-driven Lindblad equation we are able to study extremely large systems (400 spins). We find both a diffusive and a subdiffusive phase depending on the strength of the disorder and on the anisotropy parameter of the Heisenberg chain. Studying finite-size effects we show numerically and theoretically that a very large crossover length exists that controls the passage of a clean-system dominated dynamics to one observed in the thermodynamic limit. Such a large length scale, being larger than the sizes studied before, explains previous conflicting results. We also predict spatial profiles of magnetization in steady states of generic nondiffusive systems.