The renormalization-group approach for Fermi systems in the presence of singular forward scattering

Abstract

Abstract Within the framework of perturbative renormalization group, we analyze the problem of spinless fermions either coupled to a transverse gauge field or interacting through a longitudinal singular potential, in generic spatial dimensions d . The model of fermions interacting through a singular potential due to the proximity to a phase-separation instability is also discussed. We show how to develop a unified renormalization-group treatment making use of the so-called “loop cancellation”, coming from the peculiar symmetry properties of models with forward scattering. This allows to solve the renormalization-group equations and to compute the asymptotic properties of the single-particle propagator, also providing exact scaling results.