Correlation induced optimization of wave functions: The Hubbard chain

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