Large Disorder Renormalization Group Study of the Anderson Model of Localization

TL;DR

This paper introduces a large disorder renormalization group method for the 1D Anderson localization model, providing accurate calculations of spectral properties and exploring extensions to higher dimensions.

Contribution

The paper presents a novel LDRG approach based on wavefunction size, achieving asymptotic exactness and extending the method to higher dimensions.

Findings

LDRG flows to infinite disorder, ensuring accuracy.

Accurate disorder-averaged inverse participation ratio and density of states.

Modified scheme for higher dimensions, with potential for improvement.

Abstract

We describe a large disorder renormalization group (LDRG) method for the Anderson model of localization in one dimension which decimates eigenstates based on the size of their wavefunctions rather than their energy. We show that our LDRG scheme flows to infinite disorder, and thus becomes asymptotically exact. We use it to obtain the disorder-averaged inverse participation ratio and density of states for the entire spectrum. A modified scheme is formulated for higher dimensions, which is found to be less efficient, but capable of improvement.