General trial wave functions for a three body interaction

The Pfaffian wave function, which is a candidate for the 5/2 FQHE state, is the exact ground state of a short range three body model interaction, but little is known about the solutions of this model at other filling factors. Our starting point is the observation that the Pfaffian can be obtained by fully anti-symmetrizing a bilayer wave function of Halperin. A more general class of composite fermion wave functions for bilayer systems was constructed by Scarola and Jain. We find that, upon full antisymmetrization, these wave function provide a decent approximation to the low energy solutions of the three body model interaction at filling factors other than 1/2. The charged and neutral excitations of the full state are naturally constructed by creating excitations in one or both ``layers.'' We also investigate how well the ground and excited state wave functions work for the Coulomb interaction, both in the lowest and the second Landau levels. Systems with up to 18 particles are studied by a combination of exact diagonalization and Monte Carlo method.