The tight-binding model with repulsive Hubbard interactions represents an ideal prototype for the study of strong correlations. While exact numerical methods have been used with some success, they are typically limited by the size of the clusters that can be investigated or by the temperatures that can be reached. Variational methods, on the other hand, often require considerable advance knowledge of ground-state properties. The method presented here alleviates this problem by augmenting the variational approach with a scheme similar to Lanczos iterations thus bridging the gap between exact diagonalization and variational approaches. For the t-J model, the low-energy effective Hamiltonian of the Hubbard model, material properties like broken translational invariance or superconducting correlations are then investigated and a region of stability of a superconducting phase is found.
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