Umklapp scattering in fermi liquids: a renormalisation group approach

Abstract

The role of Umklapp scattering for electrons on a lattice is studied. Using renormalisation group methods it is shown that the effective low energy interaction involves not only forward scattering, but also non-forward Umklapp scattering. We show that the latter can happen to almost all of the electrons even when they have a filling of around one-half. The bahavior of these Umklapp couplings is studied in the loop expansion. It is shown that they remain marginal to all loop orders. The discussion is given in the context of two-dimensional lattices, but generalisation to three-dimensions is mentioned. We also briefly discuss the possible consequences of this on Fermi liquid theory and on physical properties of such electronic systems.