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 obtain ed as a function of the band filing up to second order in the interact ion parameter U. The k dependence of the self-energy is completely tak en into account. As a consequence, the imaginary part of the self-ener gy shows a linear behavior for fillings close to one electron per site whereas for large doping rates the quadratic omega dependence charact erizing Fermi liquids is recovered. The origin of this behavior has be en investigated analytically: linear terms associated with nesting are shown to exist in any finite-dimensional lattice although its numeric al relevance decreases very rapidly for space dimensionality larger th an 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 precis e for U values of the on-site Coulomb interaction smaller than the ban dwidth of the noninteracting spectrum.