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 (j) =〈C₉^C₉〉 of the jth Landau state in the lowest Landau level is also calculated. For =nm with m an odd integer, (j) has a period m (j) = (j+m), and there are m distinct ground states---in striking analogy with a one-dimensional charge-density-wave system. In terms of (j), profiles of the ⅓ kinks are obtained in the ground state for close to ⅓. Creation energy of the kink is obtained from the energy gap. The =12 case is markedly different.