Abstract
We propose a new formalism to solve the Hubbard Hamiltonian. The Green functions of the many-body systems is obtained from a cumulant diagrammatic expansion. The undress propagator is taken to be the exact result for a small-size cluster obtained using the Lanczos method. The inter-cluster interaction is considered to be the perturbation Hamiltonian. In 1D we reproduce some of the known results. At half filling in 2D we obtain that the system suffers a metal-insulator transition as a function of U. For a finite coordinated Bethe lattice the density of states has a three-peak shape with an Abrikosov-Suhl resonance at the Fermi level.
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