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 arrow right 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 [< or =] t' [< or =] 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 sub()cof 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> or = 0.5. The results can serve as benchmarks for controlled nonperturbative methods and guide the ongoing search for high-T sub()csuperconductivity in the Hubbard model.