A two-dimensional interacting system obeying Fractional Exclusion Statistics

TL;DR

This paper demonstrates that a two-dimensional interacting fermion system with short-range repulsion can be effectively described by noninteracting particles obeying fractional exclusion statistics, providing a new perspective on strongly correlated systems.

Contribution

It introduces a mapping of an interacting fermion system to fractional exclusion statistics using Thomas-Fermi and Hartree-Fock methods, revealing a novel equivalence.

Findings

Ground-state energies agree between Thomas-Fermi and Hartree-Fock calculations.

Interacting fermions are equivalent to noninteracting particles obeying fractional exclusion statistics.

The approach predicts energies of excited states accurately.

Abstract

We consider N fermions in a two-dimensional harmonic oscillator potential interacting with a very short-range repulsive pair-wise potential. The ground-state energy of this system is obtained by performing a Thomas-Fermi as well as a self-consistent Hartree-Fock calculation. The two results are shown to agree even for a small number of particles. We next use the finite temperature Thomas-Fermi method to demonstrate that in the local density approximation, these interacting fermions are equivalent to a system of noninteracting particles obeying the Haldane-Wu fractional exclusion statistics. It is also shown that mapping onto to a system of N noninteracting quasi-particles enables us to predict the energies of the excited states of the N-body system.