Ground State of Strongly Correlated Fermions: Short-Range Order

A new variational method is developed to calculate the ground state energy of Fermi systems with strong short-range correlations. A trial wave function of Gutzwiller's type contains additional variational parameters corresponding to configurations of pairs of nearest-neighbor sites. To evaluate the ground state energy, generalized Kikuchi's pseudo-ensemble method is used. The Hubbard model at half band-filling is investigated. The ground state energy of the paramagnetic phase is calculated for a chain, square and simple cubic lattices. It is shown that the short-range order lowers drastically the ground state energy of the Hubbard model at intermediate interaction strength. The paramagnetic phase of the Kondo-Hubbard model ($S=1/2$ and $S=5/2$) at half band-filling is investigated. The ground state energy, correlation functions and effective mass are calculated for chain, square and simple cubic lattices. A quantum phase transition was found for simple cubic lattice.