Particle-hole fluctuations in BCS-BEC crossover

Abstract

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 ${a}^{\ensuremath{-}1}=0$. 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.