Disorder and Interactions on a 1D Chain

TL;DR

This paper introduces a novel computational approach that combines transfer matrix and density matrix renormalisation group methods to study the effects of disorder and interactions on electron localization in one-dimensional systems.

Contribution

A new hybrid method integrating transfer matrix and DMRG techniques for analyzing disordered interacting electrons in 1D.

Findings

Interactions can significantly increase localization length in 1D.

The new method successfully models spinless electrons with nearest neighbor interactions.

Potential implications for understanding electron delocalization in low-dimensional systems.

Abstract

It has become increasingly clear that a full understanding of the physics of electrons in disordered systems requires an approach in which both disorder and interactions are taken into account. Work on small numbers of electrons has suggested that interactions can substantially increase the localisation length in 1 dimensional systems and possibly lead to delocalisation in 2D. It has not been clear, however, to what extent these results are applicable to systems with a finite density of electrons. Among numerical approaches the transfer matrix method combined with finite size scaling has been particularly successful for non--interacting systems, whereas the density matrix renormalisation group successfully describes interacting systems. We have developed a new approach which combines elements of both these methods and have successfully applied it to spinless electrons with nearest neighbour interactions.