Interacting Fermi systems in the strongly correlated regime play a fundamental role in many areas of physics and are of particular interest to the condensed matter community. Though weakly interacting fermions are understood, strongly correlated fermions are difficult to describe theoretically as there is no small interaction parameter to expand about. Existing strong-coupling theories rely heavily on the so-called many-body $T$-matrix approximation that sums ladder-type Feynman diagrams. Here, by acknowledging the fact that the effective interparticle interaction (i.e., the vertex function) becomes smaller above three dimensions, we propose an alternative way to reorganize Feynman diagrams and develop a theoretical framework for interacting Fermi gases beyond the ladder approximation. As an application, we solve the equation of state for three- and two-dimensional strongly interacting fermions and find excellent agreement with experimental [M. J. H. Ku et al., Science 335, 563 (2012)] and other theoretical results above temperatures of $0.5T_F$.

• Received 23 February 2016

DOI:https://doi.org/10.1103/PhysRevA.94.013610