Self-energy calculations in the Hubbard model

The authors have calculated the electronic self-energy of the two-dimensional Hubbard model as a function of frequency and momentum for various band fillings. They present this up to second order in the interaction parameter and also up to infinite order for ladder diagrams in the two-particle scattering channel. The authors have carried out direct k-space integrations using a triangle method. For a half-filled perfectly nested band, the imaginary part, lm Sigma (k_f, omega ), has a linear- omega dependence for nested Fermi surfaces which is consistent with the marginal Fermi liquid phenomenology for high-T_c superconductors. At, and near, half-filling there is a strong low-energy peak in lm Sigma ⁽²⁾(k, omega ) when k is off the Fermi surface. The physical origin of this peak is discussed. The peak is enhanced in the ladder approximation. The corresponding structure in Re Sigma ⁽²⁾(k, omega ) leads to multiple solutions of the Dyson equation for a wide range of values of the parameters. This leads to an appealing explanation of observed structure in some experimental angle-resolved photoemission spectra of high-T_c materials. The authors also find anti-bound states split off from the band in the two-particle scattering ladders consistent with the suggestion of Anderson.