NONCONVERGENCE OF THE T/U EXPANSION IN THE METALLIC PHASE OF THE HUBBARD-MODEL

We consider canonical transformations which map the Hubbard model into an effective Hamiltonian that conserves the number of doubly occupied sites. We show that the number of doubly occupied sites in the ground state of the effective Hamiltonian is without physical significance, because it may be varied arbitrarily by appropriate choice of canonical transformation. We argue that a previously given perturbation expansion for one such canonical transformation does not converge for sufficiently small values of the interaction parameter U at half filling on lattices without nesting in dimensions d > 1 and suggest that it does not converge anywhere in the nonmagnetic phase of the Hubbard model in d > 1.