Statistical Properties of The First Excited State of an Interacting Many Particle Disordered System

TL;DR

This paper investigates how the distribution of the first excitation energy in an interacting disordered electron system transitions from Wigner-Dyson to Poisson as interaction strength increases, revealing insights into many-body localization.

Contribution

It introduces a detailed analysis of the transition in excitation energy distribution using the inverse participation ratio in a disordered electron system.

Findings

Distribution $P_1$ shifts from Wigner-Dyson to Poisson with increased interaction

Inverse participation ratio characterizes the transition

Manifestation observed in a projected 2D space

Abstract

The distribution $P_1$ of the first many-body excitation energy of a weakly and moderately interacting electron gas in a finite conductor (in the diffusive regime) is calculated. As the interaction is increased, $P_1$ crosses over from Wigner-Dyson to Poisson. We characterize this transition through the inverse participation ratio in Hilbert space, and examine its manifestation in a projected 2-dimensional space.