On-Site Interaction Effects on Localization : Dominance of Non-Universal Contributions

TL;DR

This paper investigates how on-site electron-electron interactions influence localization in disordered systems, revealing that non-universal effects dominate over universal RMT predictions, especially regarding the role of electronic spin.

Contribution

It provides a combined analytical and numerical analysis showing the dominance of non-universal contributions over RMT in describing interaction effects on localization.

Findings

RMT qualitatively explains but quantitatively fails to predict interaction effects

Non-universal corrections significantly influence localization behavior

Short-range and long-range correlations cancel in RMT but not in real systems

Abstract

The influence of on-site (Hubbard) electron-electron interaction on disorder-induced localization is studied in order to clarify the role of electronic spin. The motivation is based on the recent experimental indications of a "metal-insulator" transition in two dimensional systems. We use both analytical and numerical techniques, addressing the limit of weak short-range interaction. The analytical calculation is based on Random Matrix Theory (RMT). It is found that although RMT gives a qualitative explanation of the numerical results, it is quantitatively incorrect. This is due to an exact cancellation of short range and long range correlations in RMT, which does not occur in the non-universal corrections to RMT. An estimate for these contributions is given.