The Unitary Fermi Gas at Large-N and Low Rank

We study the BCS-BEC crossover in the attractive Fermi gas using large-N techniques. Whereas the BCS and BEC limits are both well described by weakly-interacting theories, the scattering length diverges at the crossover, yielding a strongly-interacting Fermi gas. To access the physics in this strongly-interacting regime, we introduce a disordered model of N fermions coupled via M bosons, where both M,N are taken to be large. In this large-N limit we compute the electron Green's function, transition temperature, gap, and Bertsch parameter by numerically solving the system's Schwinger-Dyson equations. Further, we use the ratio gamma = M/N of bosons to fermions, also called the `rank' of the model, as a perturbative parameter to analytically study the unitary point. We compare our results to direct experimental measurements and previous mean-field studies.