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Using the dynamical mean-field theory (DMFT) as a `booster-rocket', thefunctional renormalization group (fRG) can be upgraded from a weak-couplingmethod to a powerful computation tool for strongly interacting fermion systems.The strong local correlations are treated non-perturbatively by the DMFT, whilethe fRG flow can be formulated such that it is driven exclusively by non-localcorrelations, which are more amenable to approximations. We show that the fullfrequency dependence of the two-particle vertex needs to be taken into accountin this approach, and demonstrate that this is actually possible -- in spite ofthe singular frequency dependence of the vertex at strong coupling. We are thusable to present the first results obtained from the DMFT-boosted fRG for thetwo-dimensional Hubbard model in the strongly interacting regime. We findstrong antiferromagnetic correlations from half-filling to 18 percenthole-doping, and, at the lowest temperature we can access, a sizable $d$-wavepairing interaction driven by magnetic correlations at the edge of theantiferromagnetic regime.

physical review. b./physical review. b

Antiferromagnetic and d-wave pairing correlations in the strongly  interacting two-dimensional Hubbard model from the functional renormalization  group