Second order self-energy of the two-dimensional Hubbard model

The self-energy Σ(vector k,ω) of the 2D Hubbard model on the square lattice is calculated numerically in second order perturbation theory. In the limit of small frequencies the imaginary part of Σ(vector k,ω) is also obtained analytically. We find that at half filling Im Σ(vector k,ω) ∝ω for vector k on the Fermi surface, with a logarithmically divergent prefactor close to the corners vector k = (0,±π) and (±π,0) in agreement with the numerical results. (orig.)