Anlaytic mean-field Hall crystal solution at nu=1/3: composite fermion like sub-bands and correlation effects

TL;DR

This paper presents an analytic Hartree-Fock solution for a 2DEG at filling 1/3, revealing Coulomb-induced sub-band splitting and long-range correlations, with results comparable to current models but highlighting the need for larger system sizes.

Contribution

It introduces a novel analytic Hartree-Fock approach showing Coulomb effects create sub-bands and long-range correlations in the 2DEG at filling 1/3.

Findings

Coulomb interaction splits Landau level into three sub-bands.

Localized orbitals resemble angular momentum eigenstates.

Long-range correlations require over 50 particles for convergence.

Abstract

An analytic solution of the Hartree-Fock problem for a 2DEG at filling 1/3 and half an electron per unit cell is presented. The Coulomb interaction dynamically breaks the first Landau level in three narrow sub-bands, one of which is fully occupied and the other empty, as in the composite fermion model. The localized orbitals associated to the Bloch like single electron wavefunctions are nearly static, resembling the angular momentum eigenstates within a Landau level for non-interacting fermions. Strong correlations are expected owing to the large charge density overlap between neighboring plaquettes. A numerical evaluation brings the cohesive energy close to that of the best present day models. It is also found that correlations are long range, requiring over 50 particles spread over a finite sample to approach convergence. Since presently allowed exact calculations are far from this number, the question of how relevant the considered wave-function is for the description of the ground state of the 2DEG system remains open.