EXACT-SOLUTIONS AND THE ADIABATIC HEURISTIC FOR QUANTUM HALL STATES

An operator formalism is developed for an exactly soluble model of fractional statistics, and used to show that a heuristic principle suggested earlier is rigorously valid in one particular case. For a class of model hamiltonians, Laughlin's Jastrow-type wave functions are obtained explicitly from a filled Landau level by smooth extrapolation in quantum statistics. The gap is shown not to close, which allows us to infer the incompressibility of the final states. The analysis is further extended to paired Hall states at even-denominator fillings, which arise adiabatically from an exact but unnormalizable model of superconductivity. Finally, we generalize the model to the torus geometry, and show that theorems restricting the possibilities of quantum statistics on closed surfaces are circumvented in the presence of a magnetic field.