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

Abstract

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 non-interacting energy-momentum dispersion ${\epsilon }_{\mathbf{k}}$, except for pseudogap features right at the Fermi edge. That is, it can be written as $\Sigma ({\epsilon }_{\mathbf{k}},\omega )$, with two energy-like parameters ($\epsilon$, $\omega$) instead of three ($k_x$, $k_y$ and $\omega$). The self-energy has two rather broad and weakly dispersing high energy features and a sharp $\omega ={\epsilon }_{\mathbf{k}}$ feature at high temperatures, which turns to $\omega =-{\epsilon }_{\mathbf{k}}$ at low temperatures. Altogether this yields a Z- and reversed-Z-like structure, respectively, for the imaginary part of $\Sigma ({\epsilon }_{\mathbf{k}},\omega )$. We attribute the change of the low energy structure to antiferromagnetic spin fluctuations.

13 pages, 11 figures