Emergent BCS regime of the two-dimensional fermionic Hubbard model: Ground-state phase diagram

For over half a century, the Hubbard model has played a paradigmatic role in attempts to understand quantum phenomena exhibited by correlated electrons in solids. Despite a substantial effort and the apparent simplicity of the model, its behavior in many important regimes has remained unknown. Here we study superfluidity in the two-dimensional Hubbard model with controlled error bars up to the coupling strength U = 4 and filling factor $n=0.7$ . We show, by means of unbiased diagrammatic Monte Carlo simulations, that in this regime the superfluid transition is governed by Fermi liquid physics with an emergent weak BCS-type coupling driving the instability. The corresponding ground-state phase diagram in the $(n,U)$ plane describes the competition between the superfluid states of p- and d-wave symmetry. We also report dimensionless coupling constants in this effective BCS regime