Ground-state phase diagram of the repulsive fermionic t - t ′ Hubbard model on the square lattice from weak coupling

We obtain a complete and numerically exact in the weak-coupling limit (U -> 0) ground-state phase diagram of the repulsive fermionic Hubbard model on the square lattice for filling factors 0 < n < 2 and next-nearest-neighbor hopping amplitudes 0 <= t' <= 0.5. Phases are distinguished by the symmetry and the number of nodes of the superfluid order parameter. The phase diagram is richer than may be expected and typically features states with a high-higher than that of the fundamental mode of the corresponding irreducible representation-number of nodes. The effective coupling strength in the Cooper channel lambda, which determines the critical temperature T-c of the superfluid transition, is calculated in the whole parameter space and regions with high values of lambda are identified. It is shown that besides the expected increase of lambda near the Van Hove singularity line, joining the ferromagnetic and antiferromagnetic points, another region with high values of lambda can be found at quarter filling and t' = 0.5 due to the presence of a line of nesting at t' >= 0.5. The results can serve as benchmarks for controlled nonperturbative methods and guide the ongoing search for high-T-c superconductivity in the Hubbard model.