  The fractional quantum Hall (FQH) effect is one of the most striking
phenomena in condensed matter physics. It is described by a simple Laughlin
wavefunction and has been thoroughly studied both theoretically and
experimentally. In lattice systems, however, such an effect has not been
observed, there are few simple models displaying it, and only few mechanisms
leading to it are known. Here we propose a new way of constructing lattice
Hamiltonians with local interactions and FQH like ground states. In particular,
we obtain a spin 1/2 model with a bosonic Laughlin like ground state,
displaying a variety of topological features. We also demonstrate how such a
model naturally emerges out of a Fermi-Hubbard like model at half filling, in
which the kinetic energy part possesses bands with nonzero Chern number, and we
show how this model can be implemented in an optical lattice setup with present
technology.
