Superfluid ground state phase diagram of the two-dimensional Hubbard model in the emergent Bardeen-Cooper-Schrieffer regime

In nonperturbative regimes, the superfluid instability in the two-dimensional Hubbard model can be described by an emergent BCS theory with small effective pairing constants. We compute the effective couplings using a controlled bold-line diagrammatic Monte Carlo approach, which stochastically sums all skeleton Feynman diagrams dressed in the one- and two-particle channels to high expansion orders, and map out the resulting superfluid ground-state phase diagram in a range of next-nearest-neighbor hopping \(0 \leq t^{\prime} \leq 0.3t\), interaction strength \(0 \leq U \leq 3t\), and lattice filling \(0 \leq n \leq 2\). The phase diagram is dramatically transformed in the hole-doped region and becomes particularly rich at larger doping and \(t'\). At \(t'=0.3\), the weak-coupling picture with the dominant triplet pairing sharply peaked at \(n \approx 0.73\) due to the Van Hove singularity is replaced by a plateau of the singlet \(d_{x^2-y^2}\) paring, while for \(U \gtrsim 3t\) the effective couplings are consistent with the \(d_{x^2-y^2}\) high-temperature superconductivity in the hole-doped region near cuprates' optimal doping.