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Thermodynamics of the BCS-BEC crossover

R. Haussmann·W. Rantner·S. Cerrito·W. Zwerger
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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.

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R. Haussmann, W. Rantner, S. Cerrito, W. Zwerger. 2007-02-22. Thermodynamics of the BCS-BEC crossover. https://doi.org/10.1103/physreva.75.023610

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