Effect of singular interaction terms on two-dimensional Fermi liquids

The structure of perturbation theory for an interacting two-dimensional Fermi system is analyzed, in the case where singular terms exist in the quasiparticle interactions. These give a hierarchy of singular terms in the one-particle self-energy. The dominant terms are self-consistently summed, to give a quasiparticle pole vanishing as Z(ω)∼(ω/${\mathrm{\omega }}_0$ ${)}_0^{\mathrm{\rho },\mathrm{\delta }2}$/${\mathrm{ħ}}^2$N(0)${\mathrm{\omega }}_0$ near the Fermi energy (signaling a breakdown of Fermi-liquid theory), and a form for the scattering amplitude which is consistent with the assumed form for the quasiparticle interaction.