ORBITAL OPTIMIZATION IN THE RESONATING HARTREE-FOCK APPROXIMATION ANDITS APPLICATION TO THE ONE-DIMENSIONAL HUBBARD-MODEL

A tractable direct optimization algorithm is developed to optimize orb itals in the Slater determinants (S-dets) in a resonating Hartree-Fock (Res HF) wave function. We reduce the variation space using the orbit als to put the first order energy variation in the steepest descent di rection. The orbitals in the next iteration are determined so as to mi nimize the energy functional including up to the second order variatio n. This algorithm is applied to the one dimensional Hubbard model of h alf-filling. The optimized S-dets much deviate from the trial S-dets p repared from the HF calculations. The Res HF ground state generated wi th a few S-dets explains from 99.9 to 95.0% of the ground state correl ation energy in all the correlation regimes. We have spin correlation functions with the correct short and long range behaviors and the lowe st triplet and singlet spin excitations with correct dispersions, sugg esting that the optimization of orbitals incorporates long range spin fluctuations and their mode-mode couplings.