Strong-coupling perturbation theory of the Hubbard model

The strong-coupling perturbation theory of the Hubbard model is presented a nd carried out tu order (t/U)(5) for the one-particle Green function In arb itrary dimension. The spectral weight A(k,omega) is expressed as a Jacobi c ontinued fraction and compared with new Monte-Carlo data of the one-dimensi onal, half-filled Hubbard model. Different regimes (insulator, conductor an d short-range antiferromagnet) are identified in the temperature-hopping in tegral (T, t) plane. This work completes a first paper on the subject (Phys . Rev. Lett. 80, 5389 (1998)) by providing details on diagrammatic rules an d higher-order results. In addition, the non half-filled case, infinite res ummations of diagrams and the double occupancy are discussed. Various tests : of the method are also presented.