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

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