Variational Monte Carlo analysis of the Hubbard model with a confining   potential: one-dimensional fermionic optical lattice systems
  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. 
Yusuke Fujihara, Akihisa Koga, and Norio Kawakami