Critical Spectral Statistics at the Metal-Insulator Transition in Interacting Fermionic Systems

TL;DR

This paper investigates spectral properties of disordered interacting fermionic systems, revealing a size-invariant critical level spacing distribution that varies with particle number, indicating changes in level correlations at the metal-insulator transition.

Contribution

It introduces the concept of a critical spectral distribution in interacting fermionic systems and shows its dependence on particle number and system size.

Findings

Critical level spacing distribution is invariant with system size.

Distribution depends strongly on the number of particles.

Level repulsion decreases as particle number increases.

Abstract

The spectral properties of a disordered system with few interacting three-dimensional spinless fermions are investigated. We show the existence of a critical spacings distribution which is invariant upon increase of the system size, but strongly depends on the number of particles. At the critical point, we report a substantial decrease of the degree of level repulsion as the number of particles increases indicating a decrease of nearest level correlations associated with the sparsity of the Hamiltonian matrix.