Analytic mean-field charge-density-wave solution at ν=1∕3: Composite-fermion-like subbands and correlation effects

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 subbands, one of which is fully occupied and the others empty, as in the composite fermion model. Strong correlations are expected owing to large charge density overlap between neighboring plaquettes. Numerical evaluations show an enhancement of the cohesive correlation energy, bringing the energy per particle to the proximity of that obtained in competing variational models. Correlations are long range, requiring over 98 particles in numerical computations to approach convergence.