Superconducting Response in Extended Hubbard models with π-flux Hopping

Decomposed functional renormalization group (fRG) flows allow the efficient treatment of ordering in systems with broken translational symmetry. We extend these flows into the symmetry broken regime and utilize them to study superconducting responses in the Hubbard model on the checkerboard lattice. For the models considered, the fRG allows the estimation of the order parameter up to the moderate coupling regime and shows enhancement of superconducting correlations over those calculated for Extended Hubbard interactions on the square lattice. We use the fRG to construct a preliminary phase diagram of the Hubbard model on the checkerboard lattice as a function of doping. We then catalog the sensitivity of the system response to the number of singular modes retained in the decoupling and the initial value of the symmetry breaking term for the general case of repulsive interactions on a lattice with an arbitrary flux per unit cell.