Pairing Susceptibility in the 2D Hubbard model

We compute the diagrammatic expansion of particle-particle pairing susceptibility for a Hubbard interaction on a 2D square lattice. We implement Algorithmic Matsubara Integration (AMI) to generate symbolic analytical expressions which can be evaluated without finite system approximations. We compute only vertex diagrams in the perturbative series that directly relate to pairing and probe the full external momenta dependence of the pairing susceptibility. We perform real-space Fourier transformation and study the interplay of competing symmetries (d_x²-y², d_xy, and p wave) in the weak coupling limit of the model. The symmetry projected pairing is further parameterized over a large phase space of temperature, chemical potential, and second nearest hopping and the relevant physics are discussed.