Correlation Induced Optimization of Wave Functions: the Hubbard Chain

We determine the explicit form of the single-particle Wannier functions {w$\text{}_{i}(r)}$ appearing in the parameters of quantum models. The method is illustrated on the example of the Hubbard chain, for which we derive the renormalized wave equation starting from a variational principle and by treating the system ground state energy as a functional of {w$\text{}_{i}(r)}$ and their derivatives. In this manner, the optimized basis is obtained only after the electronic correlations have been included in the rigorous Lieb-Wu solution. The results for the ground state energy and the size of the renormalized s-type orbitals, both as a function of interatomic distance, are calculated explicitly