  We introduce a two-parameter family of strongly-correlated wave functions for
bosons and fermions in lattices. One parameter, $q$, is connected to the
filling fraction. The other one, $\eta$, allows us to interpolate between the
lattice limit ($\eta=1$) and the continuum limit ($\eta\to 0^+$) of families of
states appearing in the context of the fractional quantum Hall effect or the
Calogero-Sutherland model. We give evidence that the main physical properties
along the interpolation remain the same. Finally, in the lattice limit, we
derive parent Hamiltonians for those wave functions and in 1D, we determine
part of the low energy spectrum.

Strongly Correlated Electrons;Mesoscale and Nanoscale Physics;Quantum Physics