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

• Published in: Physical review letters Vol. 117; no. 4; p. 040601
• Main Authors: Žnidarič, Marko, Scardicchio, Antonello, Varma, Vipin Kerala
• Format: Journal Article
• Language: English
• Published: United States 22.07.2016
• ISSN: 1079-7114
• DOI: 10.1103/PhysRevLett.117.040601

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.