Landau f function for the dilute Fermi gas in two dimensions

We study the Landau f function for a two-dimensional repulsive Fermi system in the dilute limit. We find the leading terms in the low-density expansion using second-order perturbation theory, following a method of Abrikosov and Khalatnikov. Further, using diagrammatic methods, we determine the essentially singular contribution coming from the two-hole bound state. The absence of a divergence in the f function, together with our earlier results on the quasiparticle lifetime, clearly demonstrates that the system is a Fermi liquid in the low-density regime.