Effects of higher-order scattering processes in BCS-BEC crossover

Proper treatment of many-body Feynman diagrams is crucial to our understanding of the physics of strongly correlated Fermi system. Theories with approximations at the T-matrix level often ignore higher-order diagrams, and may thus lead to significant quantitative inconsistency with experiment.  Here we investigate such higher-order effects via a pairing fluctuation theory of superfluidity, derived by the equations of motion approach, throughout the entire BCS-BEC crossover. We explicitly examine the direct pair–pair interaction arising from fermion exchange and find that multiple exchange processes cause screening of the pair–pair interaction. This screening depends on the fermionic scattering length. We also obtain the relation between the dimer–dimer scattering length $a_B$ and the fermionic scattering length $a_F$ in the strong-interaction limit, with the ratio $a_B/a_F$ smaller than the mean-field prediction. Meanwhile,  we also investigate the effect of higher-order vertex corrections, in addition to the Gorkov-Melik-Barkhudarov particle-hole channel, to the pairing interaction and assess their impact on pairing.  Throughout the crossover, we find that such corrections result in a significant renormalization of the pairing interaction.