  There has been a significant interest in the last years in finding fractional
quantum Hall physics in lattice models, but it is not always clear how these
models connect to the corresponding models in continuum systems. Here we
introduce a family of models that is able to interpolate between a recently
proposed set of lattice models with Laughlin-like ground states constructed
from conformal field theory and models with ground states that are practically
the usual bosonic/fermionic Laughlin states in the continuum. Both the ground
state and the Hamiltonian are known analytically, and we find that the
Hamiltonian in the continuum limit does not coincide with the usual delta
interaction Hamiltonian for the Laughlin states. We introduce quasiholes into
the models and show analytically that their braiding properties are as expected
if the quasiholes are screened. We demonstrate screening numerically for the
1/3 Laughlin model and find that the quasiholes are slightly smaller in the
continuum than in the lattice. Finally, we compute the effective magnetic field
felt by the quasiholes and show that it is close to uniform when approaching
the continuum limit. The techniques presented here to interpolate between the
lattice and the continuum can also be applied to other fractional quantum Hall
states that are constructed from conformal field theory.
