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 εₖ, except for pseudogap features right at the Fermi edge. That is, it can be written as Σ(εₖ,ω), with two energylike parameters (ε, ω) instead of three (kₓ, ky, and ω). The self-energy has two rather broad and weakly dispersing high-energy features and a sharp ω=εₖ feature at high temperatures, which turns to ω=-εₖ at low temperatures. Altogether this yields a Z- and reversed-Z-like structure, respectively, for the imaginary part of Σ(εₖ,ω). We attribute the change of the low-energy structure to antiferromagnetic spin fluctuations.