Self-energy feedback and frequency-dependent interactions in the functional renormalization group flow for the two-dimensional Hubbard model

TL;DR

This study investigates how including self-energy feedback and frequency-dependent interactions in the functional renormalization group analysis affects the flow to strong coupling in the 2D Hubbard model, revealing shifts in critical scales but consistent dominant channels.

Contribution

It is the first to incorporate both self-energy feedback and frequency-dependent interactions simultaneously in FRG flows for the 2D Hubbard model at weak to moderate coupling.

Findings

Critical scales are shifted downward when including these effects.

The leading instability channel remains largely unchanged.

Self-energies develop characteristic features during the flow.

Abstract

We study the impact of including the self-energy feedback and frequency-dependent interactions on functional renormalization group grows for the two-dimensional Hubbard model on the square lattice at weak to moderate coupling strength. Previous studies using the functional renormalization group had ignored these two ingredients to large extent, and the question is how much the flows to strong coupling analyzed by this method depend on these approximations. Here we include the imaginary part of the self-energy on the imaginary axis and the frequency-dependence of the running interactions on a frequency mesh of 10 frequencies on the Matsubara axis. We find that i) the critical scales for the flows to strong coupling are shifted downwards by a factor that is usually of order one but can get larger in specific parameter regions, and ii) that the leading channel in this flow does not depend strongly on whether self-energies and frequency-dependence is included or not. We also discuss the main features of the self-energies developing during the flows.