Functional renormalization group for commensurate antiferromagnets: Beyond the mean-field picture

TL;DR

This paper develops a functional renormalization group method for lattice fermions that accurately captures the emergence of commensurate antiferromagnetic order, surpassing mean-field limitations by incorporating feedback effects during the flow.

Contribution

It introduces a novel fRG formalism that includes feedback of the order parameter into the flow, enabling analysis beyond the mean-field approximation for antiferromagnetic states.

Findings

The new fRG method successfully captures the flow into antiferromagnetic order.

Results agree with RPA in the tested model with nested Fermi pockets.

The approach maintains accuracy using Ward identities during the flow.

Abstract

We present a functional renormalization group (fRG) formalism for interacting fermions on lattices that captures the flow into states with commensurate spin-density wave order. During the flow, the growth of the order parameter is fed back into the flow of the interactions and all modes can be integrated out. This extends previous fRG flows in the symmetric phase that run into a divergence at a nonzero RG scale, i.e., that have to be stopped at the ordering scale. We use the corresponding Ward identity to check the accuracy of the results. We apply our new method to a model with two Fermi pockets that have perfect particle-hole nesting. The results obtained from the fRG are compared with those in random phase approximation.