Particle-hole fluctuations in the BCS-BEC Crossover

TL;DR

This paper investigates particle-hole fluctuations' impact on the BCS-BEC crossover using functional renormalization, providing critical temperature estimates across the entire scattering length range and analyzing effects of Feshbach resonance widths.

Contribution

It introduces a comprehensive functional renormalization approach to quantify particle-hole fluctuations' effects on the BCS-BEC crossover and critical temperature calculations.

Findings

Critical temperature at unitarity: T_c/T_F=0.264

Particle-hole fluctuations negligible on the BEC side

Narrow Feshbach resonance reduces T_c/T_F to 0.204

Abstract

The effect of particle-hole fluctuations for the BCS-BEC crossover is investigated by use of functional renormalization. We compute 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 later 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.