BCS-BEC crossover in a relativistic boson-fermion model beyond mean field approximation

TL;DR

This paper explores the effects of quantum fluctuations on the BCS-BEC crossover in a relativistic superfluid, revealing that fluctuations induce a first-order phase transition and significantly alter the crossover characteristics.

Contribution

It extends the relativistic boson-fermion model beyond mean field by incorporating fluctuations via CJT formalism, affecting the phase transition nature and crossover properties.

Findings

Fluctuations turn the superfluid transition into a first-order phase transition.

The crossover properties are significantly modified by quantum fluctuations.

Critical temperature and particle abundances depend on the boson mass.

Abstract

We investigate the fluctuation effect of the di-fermion field in the crossover from Bardeen-Cooper-Schrieffer (BCS) pairing to a Bose-Einstein condensate (BEC) in a relativistic superfluid. We work within the boson-fermion model obeying a global U(1) symmetry. To go beyond the mean field approximation we use Cornwall-Jackiw-Tomboulis (CJT) formalism to include higher order contributions. The quantum fluctuations of the pairing condensate is provided by bosons in non-zero modes, whose interaction with fermions gives the two-particle-irreducible (2PI) effective potential. It changes the crossover property in the BEC regime. With the fluctuations the superfluid phase transition becomes the first order in grand canonical ensemble. We calculate the condensate, the critical temperature $T_{c}$ and particle abundances as functions of crossover parameter the boson mass.