Ground-state degeneracy and fractionally charged excitations in the anomalous quantum Hall effect

The Hamiltonian describing two-dimensional electrons in a high magnetic field is diagonalized exactly for a small number of particles. In addition to the energy spectrum the mean occupation number ρ(j)=〈Cⱼ^Cⱼ〉 of the jth Landau state in the lowest Landau level is also calculated. For ν=n/m with m an odd integer, ρ(j) has a period m [ρ(j)=ρ(j+m)], and there are m distinct ground states---in striking analogy with a one-dimensional charge-density-wave system. In terms of ρ(j), profiles of the ⅓ kinks are obtained in the ground state for ν close to ⅓. Creation energy of the kink is obtained from the energy gap. The ν=1/2 case is markedly different.