Functional renormalization group approach to the BCS-BEC crossover

TL;DR

This paper employs a functional renormalization group method to analyze the BCS-BEC crossover in ultracold fermionic gases, capturing both few-body and many-body physics across different scales.

Contribution

It introduces a non-perturbative flow equation framework that unifies microscopic and macroscopic descriptions of the BCS-BEC crossover.

Findings

Computed the phase diagram as a function of scattering length and temperature.

Determined the gap, correlation length, and molecular scattering length.

Observed universal behavior near the critical temperature.

Abstract

The phase transition to superfluidity and the BCS-BEC crossover for an ultracold gas of fermionic atoms is discussed within a functional renormalization group approach. Non-perturbative flow equations, based on an exact renormalization group equation, describe the scale dependence of the flowing or average action. They interpolate continuously from the microphysics at atomic or molecular distance scales to the macroscopic physics at much larger length scales, as given by the interparticle distance, the correlation length, or the size of the experimental probe. We discuss the phase diagram as a function of the scattering length and the temperature and compute the gap, the correlation length and the scattering length for molecules. Close to the critical temperature, we find the expected universal behavior. Our approach allows for a description of the few-body physics (scattering and molecular binding) and the many-body physics within the same formalism.