Thermodynamics of the BCS-BEC crossover

TL;DR

This paper develops a self-consistent, conserving, and gapless theoretical framework for the thermodynamics of the BCS-BEC crossover, covering both normal and superfluid phases, and compares well with existing numerical and field-theoretic results.

Contribution

It introduces a variational many-body formalism with a ladder approximation to analyze the entire BCS-BEC crossover thermodynamics.

Findings

Critical temperature and equation of state are computed across the crossover.

Tightly bound pairs are described by a Popov-type approximation for dilute Bose gases.

Results align with recent numerical and field-theoretic studies at unitarity.

Abstract

We present a self-consistent theory for the thermodynamics of the BCS-BEC crossover in the normal and superfluid phase which is both conserving and gapless. It is based on the variational many-body formalism developed by Luttinger and Ward and by DeDominicis and Martin. Truncating the exact functional for the entropy to that obtained within a ladder approximation, the resulting self-consistent integral equations for the normal and anomalous Green functions are solved numerically for arbitrary coupling. The critical temperature, the equation of state and the entropy are determined as a function of the dimensionless parameter $1/k_Fa$, which controls the crossover from the BCS-regime of extended pairs to the BEC-regime of tightly bound molecules. The tightly bound pairs turn out to be described by a Popov-type approximation for a dilute, repulsive Bose gas. Even though our approximation does not capture the critical behaviour near the continuous superfluid transition, our results provide a consistent picture for the complete crossover thermodynamics which compare well with recent numerical and field-theoretic approaches at the unitarity point.