An exactly solvable model for fractional quantum Hall effect

We present a model Hamiltonian for spinless electrons in a magnetic field with strong short-range interaction that lends itself to exact solutions for all low-energy states at arbitrary filling factor $\nu < 1/2p$.The model produces incompressible states at $\nu = n/(2pn + 1)$, where $n$ and $p$ are integers - precisely the filling fractions where fractional quantum Hall effect occurs. We present numerical evidence showing that the fractional quantum Hall ground states of this model are adiabatically connected, and thus topologically equivalent to the Coulomb ground states in the lowest Landau level.