Momentum structure of the self-energy and its parametrization for the two-dimensional Hubbard model

We compute the self-energy for the half-filled Hubbard model on a square lattice using lattice quantum Monte Carlo simulations and the dynamical vertex approximation. The self-energy is strongly momentum-dependent, but it can be parametrized via the noninteracting energy-momentum dispersion [epsilon]k, except for pseudogap features right at the Fermi edge. That is, it can be written as [Sigma]([epsilon]k,[omega]), with two energylike parameters ([epsilon], [omega]) instead of three (kx, ky, and [omega]). The self-energy has two rather broad and weakly dispersing high-energy features and a sharp [omega]=[epsilon]k feature at high temperatures, which turns to [omega]=-[epsilon]k at low temperatures. Altogether this yields a Z- and reversed-Z-like structure, respectively, for the imaginary part of [Sigma]([epsilon]k,[omega]). We attribute the change of the low-energy structure to antiferromagnetic spin fluctuations.