  We investigate the one-dimensional Hubbard model with a confining potential,
which may describe cold fermionic atoms trapped in an optical lattice.
Combining the variational Monte Carlo simulations with the new stochastic
reconfiguration scheme proposed by Sorella, we present an efficient method to
systematically treat the ground state properties of the confined system with a
site-dependent potential. By taking into account intersite correlations as well
as site-dependent on-site correlations, we are able to describe the coexistence
of the metallic and Mott insulating regions, which is consistent with other
numerical results. Several possible improvements of the trial states are also
addressed.
