MEAN-FIELD APPROXIMATION FOR ANYONS IN A MAGNETIC-FIELD

The mean field equations for anyons in an external homogeneous magneti c field are studied and two classes of mean field solutions are explic itly constructed. The first class of solutions, corresponding to one f illed Landau level in the combined external and smeared out statistica l magnetic fields, is compared to the corresponding exact groundstate solutions. The energies are found to agree well at low densities and w hen the statistical field is not too strong compared to the background field. At high densities the fermi pressure increases the mean field energy indefinitely. The mean field solutions also miss the lower part of the energy spectrum. To the second class of mean field solutions n o corresponding anyon state is known. These solutions represent the an yonic continuation of the fermi state with two filled Landau levels.