Renormalized mean-field analysis of antiferromagnetism and d-wave superconductivity in the two-dimensional Hubbard model

TL;DR

This paper combines renormalization group and mean-field methods to study the competition and coexistence of antiferromagnetism and d-wave superconductivity in the 2D Hubbard model, revealing limited coexistence regions and the emergence of triplet pairing.

Contribution

It introduces a novel combined approach using functional renormalization group and mean-field theory to analyze competing orders in the Hubbard model.

Findings

Antiferromagnetism and superconductivity suppress each other.

Limited parameter space for coexistence of both orders.

Triplet pi-pairing appears in the coexistence region.

Abstract

We analyze the competition between antiferromagnetism and superconductivity in the two-dimensional Hubbard model by combining a functional renormalization group flow with a mean-field theory for spontaneous symmetry breaking. Effective interactions are computed by integrating out states above a scale Lambda_{MF} in one-loop approximation, which captures in particular the generation of an attraction in the d-wave Cooper channel from fluctuations in the particle-hole channel. These effective interactions are then used as an input for a mean-field treatment of the remaining low-energy states, with antiferromagnetism, singlet superconductivity and triplet pi-pairing as the possible order parameters. Antiferromagnetism and superconductivity suppress each other, leaving only a small region in parameter space where both orders can coexist with a sizable order parameter for each. Triplet pi-pairing appears generically in the coexistence region, but its feedback on the other order parameters is very small.