title: Interacting fermions in two dimensions: beyond the perturbation theory.
abstract: We consider a system of 2D fermions with a short-range interaction. A straightforward perturbation theory is shown to be ill defined even for an infinitesimally weak interaction, as the perturbative series for the self-energy diverges near the mass shell. We show that the divergences result from the interaction of fermions with the zero-sound collective mode. By resumming the most divergent diagrams, we obtain a closed form of the self-energy near the mass shell. The spectral function exhibits a threshold feature at the onset of the emission of the zero-sound waves. We also show that the interaction with the zero sound does not affect a nonanalytic, T2 part of the specific heat.
authors.affiliation: Department of Physics, University of Florida, P.O. Box 118440, Gainesville, Florida 32611-8440, USA.
authors.forename: Suhas
authors.initials: S
authors.lastname: Gangadharaiah
authors.forename: Dmitrii L
authors.initials: DL
authors.lastname: Maslov
authors.forename: Andrey V
authors.initials: AV
authors.lastname: Chubukov
authors.forename: Leonid I
authors.initials: LI
authors.lastname: Glazman