Umklapp processes for electrons and their renormalization-group flow

Abstract

We study umklapp couplings and their renormalization-group flow for electrons in a two-dimensional lattice. It is shown that the effective low-energy Hamiltonian involves not only forward scattering, but also considerable nonforward umklapp scattering, when the electrons fill a substantial fraction of the valence band. The behavior of these couplings under the renormalization group is studied in the loop expansion. It is shown that they remain marginal. We conclude with the possible consequences of this on properties of such electronic systems and their Fermi-liquid theory.