Correlated Basis Function method for fermions on a lattice: applications to the Hubbard model

We introduce a new lattice version of the Correlated Basis Function ( CBF) approach for the study of strongly interacting electrons. As a first application we have chosen the 1 dimensional Hubbard model. For this system, we have implemented different types of correlations, namely a) Gutzwiller; b) J astrow; c) nearest-neighbor spin-spin; and d) excitonic ( "ed") on the Fermi sea. Correlated BOS and Spin-Density-Wave (SDW) theories have also been developed. The resulting energies, momentum distribution and other quantities are compared with exact results (when available), and are discussed, both from the point of view of the method, as well as from a physical view point. The most important correlations that are needed to obtain good ground state energies are found to be Gutzwiller (reduced double occupancy) plus "ed" attractive correlations (between empty and doubly occupied sites), in agreement with other studies.