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

TL;DR

This paper analyzes the momentum-dependent self-energy in the half-filled 2D Hubbard model using quantum Monte Carlo and dynamical vertex approximation, revealing a parametrization based on non-interacting dispersion and temperature-dependent features.

Contribution

It introduces a parametrization of the self-energy as a function of energy-like parameters, simplifying the understanding of its momentum dependence in the Hubbard model.

Findings

Self-energy can be parametrized as (_k, ) with two energy parameters.

High energy features are broad and weakly dispersing.

Low energy structure changes from =_k to =-_k with decreasing temperature.

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 $\varepsilon_{\mathbf{k}}$, except for pseudogap features right at the Fermi edge. That is, it can be written as $\Sigma(\varepsilon_{\mathbf{k}},\omega)$, with two energy-like parameters ($\varepsilon$, $\omega$) 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 $\omega= \varepsilon_{\mathbf{k}}$ feature at high temperatures, which turns to $\omega= -\varepsilon_{\mathbf{k}}$ at low temperatures. Altogether this yields a Z- and reversed-Z-like structure, respectively, for the imaginary part of $\Sigma(\varepsilon_{\mathbf{k}},\omega)$. We attribute the change of the low energy structure to antiferromagnetic spin fluctuations.