Exact results for the fractional quantum Hall effect with general interactions

Abstract

Laughlin's state ${\ensuremath{\psi}}_{m}$ is shown to be the exact nondegenerate ground state for repulsive interactions of vanishing range. In this limit, his quasihole states are not exact, and some previously proposed states are ruled out. An experimental prediction is made concerning the competition of ${\ensuremath{\psi}}_{m}$ with charge-density waves. Several exact properties are shared by systems with interactions of shorter range than ${r}^{\mathrm{\ensuremath{-}}2}$, for which the center-of-mass motion separates from the other degrees of freedom. These include new invariant subspaces, an operator that creates exact eigenstates, and a subset property of the energy eigenvalues.