Random one-body approximation to the Hubbard model. I. Formalism

Abstract

An approximation scheme is presented for treating the Hubbard Hamiltonian through an effective selfconsistent random potential. The random variables determining the effective potential are statistically correlated to simulate many-body correlations. The formalism is developed in detail for the half-filled Hubbard model; it is shown that the proposed scheme reproduces exactly the metallic and atomic limits and interpolates between the two.