Diffusive and Subdiffusive Spin Transport in the Ergodic Phase of a Many-Body Localizable System

TLDR

High‑temperature spin transport in a disordered Heisenberg chain is studied in the ergodic regime. The authors aim to predict spatial magnetization profiles in steady states of generic nondiffusive systems. They employ density‑matrix renormalization group on the boundary‑driven Lindblad equation to analyze stationary states of up to 400 spins and finite‑size effects, revealing a large crossover length. The work identifies diffusive and subdiffusive transport phases governed by disorder strength and anisotropy, with a large crossover length that resolves previous conflicting results.

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.