General validity of Jastrow-Laughlin wave functions

We construct a class of interacting-boson Hamiltonians whose exact ground-state wave functions are of Jastrow form. These Hamiltonians generally have both two- and three-body interactions; however, we show that the three-body interaction does not affect the long-wavelength physics. This enables us to deduce that (a) for Coulomb interacting bosons at T=0 the lower critical dimension is dc=2; (b) in two dimensions, the ground-state wave function has the form of the modulus of the Laughlin wave function and exhibits algebraic long-range order; and (c) for short-range repulsions, we obtain a simple expression for the sound velocity. We also show that the Laughlin wave function is the generic ground-state wave function for fermions in a magnetic field corresponding to a filling factor of {ν}=1/q.