Statistics of energy spectra of a strongly disordered system of interacting electrons

TL;DR

This paper investigates how the energy level statistics of a finite two-dimensional disordered electron system transition from Poisson to Wigner distribution as disorder decreases, indicating a delocalization crossover linked to exciton formation.

Contribution

It provides a numerical analysis of the energy level statistics transition in a 2D disordered electron system and relates it to exciton delocalization phenomena.

Findings

Energy level statistics shift from Poisson to Wigner with decreasing disorder.

The transition coincides with the one-electron delocalization crossover.

Delocalization occurs in the space of occupation numbers of electron-hole pairs.

Abstract

Statistics of many particle energy levels of a finite two-dimensional system of interacting electrons is numerically studied. It is shown that the statistics of these levels undergoes a Poisson to Wigner crossover as the strength of the disorder is decreased. This transition occurs at a similar strength of disorder as the one-electron delocalization crossover in a finite 2d system and develops almost simultaneously at all energies. We interpret this crossover in terms of delocalization in the space of occupation numbers of strongly bound and compact electron-hole pairs (excitons).