J. Galan et al., 2ND-ORDER SELF-ENERGY OF THE HUBBARD HAMILTONIAN - ABSENCE OF QUASI-PARTICLE EXCITATIONS NEAR HALF-FILLING, Physical review. B, Condensed matter, 48(18), 1993, pp. 13654-13660
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.