S. Daul et M. Dzierzawa, 2ND-ORDER SELF-ENERGY OF THE 2-DIMENSIONAL HUBBARD-MODEL, Zeitschrift fur Physik. B, Condensed matter, 103(1), 1997, pp. 41-44
The self-energy Sigma(k,omega) of the 2D Hubbard model on the square l
attice is calculated numerically in second order perturbation theory.
In the limit of small frequencies the imaginary part of Sigma(k,omega)
is also obtained analytically. We find that at half filling Im Sigma(
k,omega) similar to omega for k on the Fermi surface, with a logarithm
ically divergent prefactor close to the corners k = (0, +/-pi) and (+/
-pi, 0) in agreement with the numerical results.