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

摘要

We study the impact of including self-energy feedback and frequency-dependent interactions on functional renormalization group flows 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 twa ingredients to a 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 downward by a factor that is usually of order 1 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.