Particle-hole fluctuations in BCS-BEC crossover

The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute the Gorkov effect and the critical temperature for the whole range in the scattering length a. On the BCS side for small negative a we recover the Gorkov approximation, while on the BEC side of small positive a the particle-hole fluctuations play no important role, and we find a system of interacting bosons. In the unitarity limit of infinite scattering length our quantitative estimate yields T_c/T_F=0.264. We also investigate the crossover from broad to narrow Feshbach resonances—for the latter we obtain T_c/T_F=0.204 for a⁻¹=0. A key ingredient for our treatment is the computation of the momentum dependent four-fermion vertex and its bosonization in terms of an effective bound-state exchange.