Self-energy flows in the two-dimensional repulsive Hubbard model

TL;DR

This paper employs advanced functional renormalization group techniques to analyze the two-dimensional repulsive Hubbard model, emphasizing the full frequency dependence of self-energy and interaction vertices, revealing key effects at phase transitions.

Contribution

It introduces a method to compute the full Matsubara frequency dependence of self-energy and interaction vertices without simplifying assumptions, improving the understanding of phase transitions in the Hubbard model.

Findings

Self-energy frequency dependence is crucial at the ferromagnetism to d-wave superconductivity transition.

Fermi surface deformations are minor at Van Hove filling.

Non-Fermi-liquid exponents are identified at the transition point.

Abstract

We study the two-dimensional repulsive Hubbard model by functional RG methods, using our recently proposed channel decomposition of the interaction vertex. The main technical advance of this work is that we calculate the full Matsubara frequency dependence of the self-energy and the interaction vertex in the whole frequency range without simplifying assumptions on its functional form, and that the effects of the self-energy are fully taken into account in the equations for the flow of the two-body vertex function. At Van Hove filling, we find that the Fermi surface deformations remain small at fixed particle density and have a minor impact on the structure of the interaction vertex. The frequency dependence of the self-energy, however, turns out to be important, especially at a transition from ferromagnetism to d-wave superconductivity. We determine non-Fermi-liquid exponents at this transition point.