  Motivated by experiments on atomically smooth layers of LaTiO$_3$, a Mott
insulator, sandwiched between layers of SrTiO$_3$, a band insulator, a simple
model for such heterostructures is studied using quasi one-dimensional lattices
and the Lanczos method. Taking both the local and long-range Coulomb
interactions into account, and computing the layer dependent local density of
states, a metallic state was found at the interface whose extent strongly
depends on the dielectric constant of the material. We also observed that the
antiferromagnetic correlations in the bulk Mott phase persist into the metallic
region. Our conclusions are in excellent agreement with recently reported
results for this model in the opposite limit of infinite dimensions, thus
providing an alternative tool to study electronic reconstruction effects in
heterostructures.
