Comparative study of many-body t-matrix theories for a Fermi gas through the BCS-BEC crossover

In the latest several years, diagrammatic theories based on the t-matrix approximation with different degrees of self-consistency have been developed to describe a Fermi gas through the BCS-BEC crossover. A comprehensive comparison between the results obtained by the different approaches for both thermodynamical and dynamical quantities is, however, still lacking. In the present work, we consider all the possible ways of implementing self-consistency in the t-matrix approximation and compare the outcomes of the different approaches between each other (and with the available experimental and Quantum Monte Carlo data) through the whole BCS-BEC crossover. In this way, we expect to provide a guideline on the virtues and the drawbacks of each scheme that can help future research in this field.