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This thesis is concerned with ground state properties of two-dimensionalfermionic superfluids, in which fluctuation effects like the renormalization ofthe order parameter or infrared singularities are important. In the superfluidstate, the fermionic two-particle vertex develops rich and singular dependenceson momentum and frequency, for which an efficient parametrization in terms ofboson-exchange interactions in the particle-hole and particle-particle channelsis formulated. Based on this decomposition of the vertex, flow equations forthe effective interactions are derived, extending existingchannel-decomposition schemes to i) the description of symmetry breaking in theCooper channel and ii) the inclusion of those two-loop renormalizationcontributions to the vertex that are neglected in the Katanin scheme. In thesecond part of this thesis, the superfluid ground state of various modelsystems is studied. For the attractive Hubbard model at weak coupling, themomentum and frequency dependence of the two-particle vertex and the frequencydependence of the self-energy are determined on one- and two-loop level.Results for the suppression of the superfluid gap by fluctuations are in goodagreement with the literature. The two-loop approximation captures the singularinfrared behaviour that is expected in a fermionic superfluid at zerotemperature. For the repulsive Hubbard model at weak coupling, the momentumdependence of the two-particle vertex and the d-wave superfluid gap aredetermined on one-loop level as a function of the interaction, the next-nearestneighbour hopping and the fermionic density. The results for the criticalscales and superfluid gaps are in qualitative agreement with the literature andsuggest the existence of an optimal value of the next-nearest neighbour hoppingfor pairing.

Functional renormalization group study of fluctuation effects in fermionic superfluids