A simple crossing-symmetric approximation for the fully reducible vertex is compared with Monte Carlo simulations of the two-dimensional Hubbard model. Up to quarter-filling, in the intermediate coupling regime, accuracies better than 10\% are obtained for several static correlation functions, including spin and charge, as well as the pairing channels most widely studied in the context of high-T(c) superconductivity. The accuracy is generally better for the pairing channels. The results shed light on the applicability of the renormalized generalized-random-phase-approximation scheme, its relation to Fermi-liquid theory, and on the regime where nontrivial effects may appear in pairing channels. The approximation under study consists in assuming that for parallel spins the fully reducible particle-particle vertex vanishes, while for antiparallel spins it is equal to the T matrix. The fully reducible particle-hole vertex is then obtained from the latter vertex by using crossing symmetry. This simple approximation is not conserving but it preserves global symmetries. It suggests that Monte Carlo results for the two-dimensional Hubbard model in small systems at low density and intermediate coupling can be interpreted using a weakly correlated Fermi-liquid picture.

}, author = {Dar{\'e}, A. M. and Chen, L. and A.-M. S. Tremblay} }