Fermionic two-loop functional renormalization group for correlated fermions: Method and application to the attractive Hubbard model

TL;DR

This paper introduces an advanced two-loop functional renormalization group method for correlated fermions, effectively capturing collective excitations, symmetry-breaking, and fluctuation effects, demonstrated on the attractive Hubbard model.

Contribution

It develops a novel two-loop FRG approach for fermions that treats all channels equally and captures collective mode physics, improving upon one-loop approximations.

Findings

Superfluid gaps are reduced by fluctuations compared to one-loop results.

The method captures the renormalization of the amplitude mode by phase fluctuations.

Application to the attractive Hubbard model demonstrates the method's effectiveness.

Abstract

We derive an efficient method for treating renormalization contributions at two-loop level within the functional renormalization group in the one-particle irreducible formalism for fermions. It is based on a decomposition of the two-particle vertex in charge, magnetic and pairing channels. The method treats single-particle and collective excitations in all channels on equal footing, allows for the description of symmetry-breaking and captures collective mode fluctuation physics in the infrared. As a first application, we study the superfluid ground state of the two-dimensional attractive Hubbard model. We obtain superfluid gaps that are reduced by fluctuations in comparison to the one-loop approximation and demonstrate that the method captures the renormalization of the amplitude mode by long-range phase fluctuations.