Optimization of single-particle basis for exactly soluble models of correlated electrons

We determine the explicit form of the single-particle wave functions {w(i)( r)} appearing in the microscopic parameters of models in the second-quantiz ation representation. Namely, the general form of the renormalized wave equ ation is derived from the Lagrange-Euler principle by treating the system g round-state energy of an exact correlated state as a functional of {w(i)(r) } and their derivatives. The method is applied to three model situations wi th one orbital per atom. For the first example-the Hubbard chain-the optimi zed basis is obtained only after the electronic correlation has been includ ed in the rigorous Lieb-Wu solution for the ground-state energy. The renorm alized Wannier wave functions are obtained variationally starting from the atomic basis for the s-type wave functions. The principal characteristics s uch as the ground-state energy and the model parameters are calculated as a function of interatomic distance. Second, the atomic systems such as the H -2 molecule or He atom can be treated in the same manner and the optimized orbitals are obtained to illustrate the method further. Finally, we illustr ate the method by solving exactly correlated quantum dots of N less than or equal to 8 atoms with the subsequent optimization of the orbitals. Our met hod may be regarded as the next step in analyzing exactly soluble many-body models that provides properties as a function of the lattice parameter and defines at the same Lime the renormalized wave function for a single parti cle.