Entangled magnetic, charge, and superconducting pairing correlations in the two-dimensional Hubbard model: a functional renormalization-group analysis

TL;DR

This study employs a multiloop functional renormalization group approach to analyze magnetic, charge, and superconducting correlations in the 2D Hubbard model, revealing the interplay of fluctuations and pairing mechanisms.

Contribution

It introduces a multiloop extension of the functional renormalization group to analyze susceptibilities and their channel contributions in the 2D Hubbard model.

Findings

Antiferromagnetic fluctuations influence d-wave superconductivity.

Channel contributions reveal the interplay between magnetic, charge, and pairing correlations.

Analytical understanding of susceptibility behavior with temperature and interaction strength.

Abstract

Using the recently introduced multiloop extension of the functional renormalization group, we compute the magnetic, density, and superconducting susceptibilities of the two-dimensional Hubbard model at weak coupling and present a detailed analysis of their evolution with temperature, interaction strength, and loop order. By breaking down the susceptibilities into contributions from the bare susceptibility and the individual channels, we investigate their relative importance as well as the channel interplay. In particular, we trace the influence of antiferromagnetic fluctuations on the $d$-wave superconductivity and provide an analytical understanding for the observed behavior.