Antiferromagnetic and d-wave pairing correlations in the strongly interacting two-dimensional Hubbard model from the functional renormalization group

TL;DR

This paper combines dynamical mean-field theory with the functional renormalization group to study strongly interacting two-dimensional Hubbard models, revealing antiferromagnetic and d-wave pairing correlations.

Contribution

It introduces a DMFT-boosted fRG approach that accurately captures non-local correlations in strongly interacting fermion systems, including full frequency dependence of the vertex.

Findings

Strong antiferromagnetic correlations from half-filling to 18% hole doping

Detection of sizable d-wave pairing interaction driven by magnetic correlations

First results demonstrating the effectiveness of the combined DMFT-fRG method in strongly correlated regimes

Abstract

Using the dynamical mean-field theory (DMFT) as a `booster-rocket', the functional renormalization group (fRG) can be upgraded from a weak-coupling method to a powerful computation tool for strongly interacting fermion systems. The strong local correlations are treated non-perturbatively by the DMFT, while the fRG flow can be formulated such that it is driven exclusively by non-local correlations, which are more amenable to approximations. We show that the full frequency dependence of the two-particle vertex needs to be taken into account in this approach, and demonstrate that this is actually possible -- in spite of the singular frequency dependence of the vertex at strong coupling. We are thus able to present the first results obtained from the DMFT-boosted fRG for the two-dimensional Hubbard model in the strongly interacting regime. We find strong antiferromagnetic correlations from half-filling to 18 percent hole-doping, and, at the lowest temperature we can access, a sizable $d$-wave pairing interaction driven by magnetic correlations at the edge of the antiferromagnetic regime.