A PAIRWISE APPROXIMATION IN THE HUBBARD-MODEL

The Hubbard Hamiltonian is projected onto a representation consisting of electron pairs characterised by the momentum of their centre of mas s. Within this approximation the electron gas can be viewed as a colle ction of subsets, each of which contains a constant number of electron pairs, all having the same centre of mass momentum. As these subsets are decoupled, the Hubbard Hamiltonian is diagonalised to give two typ es of many-body eigenstates: correlated and uncorrelated. The uncorrel ated pairs build up an ideal Fermi gas. Excellent agreement is found f or the uncorrelated energy calculated at zero temperature in one dimen sion between this model and the Bethe ansatz, for arbitrary electron c oncentration and magnitude of the electron interaction. The correlated states turn out to be of the BCS type.