Lee-Yang cluster expansion approach to the BCS-BEC crossover: BCS and BEC limits

Abstract

It is shown that a cluster expansion technique, which is usually applied in the high-temperature regime to calcutate virial coefficients, can be applied to evaluate the superfluid transition temperature of the BCS-BEC crossoverà la Lee and Yang. The transition temperature is identified with the emergence of the singularity in the sum of a certain infinite series of cluster functions. In the weak-coupling limit, we reproduce the Thouless criterion and the number equation of Nozières and Schmitt-Rink, and hence the transition temperature of the BCS theory. In the strong-coupling limit, we reproduce the transition temperature of Bose-Einstein condensation of non-interacting tightly bound dimers.

Perron-Frobenius theorem on the superfluid transition of an ultracold Fermi gas

“…From the Perron-Frobenius theorem (ii) and Theorem 2, it is found that there exists a unique fugacity at the phase transition point for any a. Physically this implies that there is no fragmentation of Bose-Einstein condensates of dimers and Cooper pairs at the ladder-approximation level of Lee-Yang contracted 0-graphs. Besides, we can show [19] that the thermodynamic potential, which is calculated at the ladder-approximation level of the Lee-Yang contracted 0-graphs and in the first-order approximation in the coupling constant of U (2) , is identical to the results of Nozieres and Schmitt-Rink (NSR) [27,28], which include the effect of the Gaussian fluctuations of Cooper pairs. Hence, our result indicates that if we only consider the range of Gaussian fluctuations of Cooper pairs, there is no fragmentation in the BCS-BEC crossover.…”

“…According to the quantum cluster expansion method of Lee and Yang [15,16], the grand partition function is calculated by the cluster functions U (1) , U (2) , etc., and expressed by the Lee-Yang contracted 0-graphs. In this study, we consider an infinite series of the ladder-type Lee-Yang contracted 0-graphs, which gives the noninteracting dimer BEC transition temperature in BEC limit [17,18], and the BCStransition temperature in BCS limit [19]. To investigate the phase transition of the system, we analyze a singularity of an infinite series of ladder-type Lee-Yang contracted 0-graphs.…”

Universal relations for spin-orbit-coupled Fermi gases in two and three dimensions

“…(80) which reduces to the results in the absence of the SO coupling for s-and p-wave interactions, respectively [9,13,31,59,60].…”

Cluster expansion method and its application in computational materials science

“…The phase diagram consists of two miscibility gaps at low temperature, the first between Fe 1Ày Mn y PO 4 (denoted by a) and Li y Fe 1Ày Mn y PO 4 (denoted by SS) and the second between Li y Fe 1Ày Mn y PO 4 (SS) and LiFe 1Ày Mn y PO 4 (denoted by b), where 0 6 y 6 1. [75]. Lohmann calculated the exponential decay of correlations for quite general single scale spin systems by cluster expansion [76].…”