Towards a cluster extension of DMF²RG and its application to the Hubbard model: Concepts and first results

The DMF²RG has been introduced to overcome the weak-coupling limitation of the functional renormalization group (fRG) and builds on the idea of exploiting the dynamical mean field theory (DMFT) as starting point for the fRG flow equations. This approach allows to capture non-perturbative local correlations via DMFT together with perturbative non-local correlations generated during the flow. We illustrate how this approach can be extended to grasp non-perturbative non-local correlations by instead employing the cellular DMFT (CDMFT) solution of the 2d Hubbard model on a 2x2 cluster as a starting point. Using the recently introduced single-boson-exchange (SBE) decomposition of the two-particle vertex, we reformulate the vertex flow equation in terms of Yukawa couplings, bosonic propagators and a residual fermionic four-point vertex, offering both interpretative and computational advances. We investigate the renormalization of the flowing correlation functions by numerically solving the fRG equations and show first results in the weak-coupling regime at half-filling.