2ND-ORDER SELF-ENERGY OF THE HUBBARD HAMILTONIAN - ABSENCE OF QUASI-PARTICLE EXCITATIONS NEAR HALF-FILLING

The electron self-energy SIGMA(k, omega) corresponding to the one-band Hubbard Hamiltonian on clusters of the square lattice has been obtained as a function of the band filing up to second order in the interaction parameter U. The k dependence of the self-energy is completely taken into account. As a consequence, the imaginary part of the self-energy shows a linear behavior for fillings close to one electron per site whereas for large doping rates the quadratic omega dependence characterizing Fermi liquids is recovered. The origin of this behavior has been investigated analytically: linear terms associated with nesting are shown to exist in any finite-dimensional lattice although its numerical relevance decreases very rapidly for space dimensionality larger than two. Implications of these results on the renormalization factor Z have been analyzed. From a practical point of view, we conclude that a standard second-order perturbative treatment is quantitatively precise for U values of the on-site Coulomb interaction smaller than the bandwidth of the noninteracting spectrum.