Diffusion in the Anderson model in higher dimensions

TL;DR

This paper introduces an advanced numerical method to evaluate diffusion properties in high-dimensional disordered systems, enabling analysis of systems with over a million sites and revealing incoherent diffusion behavior near localization transitions.

Contribution

The extended microcanonical Lanczos method allows direct computation of diffusion constants in large-scale high-dimensional Anderson models, surpassing previous computational limitations.

Findings

Confirmed dynamical scaling behavior below localization transition

Identified a broad region of incoherent diffusion

Demonstrated the method's capability for systems with over 10^6 sites

Abstract

We present an extended microcanonical Lanczos method (MCLM) for a direct evaluation of the diffusion constant and its frequency dependence within the disordered Anderson model of noninteracting particles. The method allows to study systems beyond $10^6$ sites of hypercubic lattices in $ d = 3- 7$ dimensions. Below the transition to localization, where we confirm dynamical scaling behavour, of interest is a wide region of incoherent diffusion, similar to percolating phenomena and to interacting many-body localized systems.