Ground-state properties of the Hubbard model by Lanczos diagonalizations

We investigate the Hubbard model on a two-dimensional cluster of 18 sites using Lanczos algorithm for different strengths of Coulomb repulsion in the low doping region. Energies and correlation functions are given for half-filling and two holes. In the strong coupling regime we compare our results with the $t-J$ model. We confirm the tendency of holes to repel, although a significant value of the $d_{x^2-y^2}$-wave superconductive order parameter is measured. These data represent a benchmark for future quantum simulations.