Umklapp Processes for Electrons and Their Renormalisation Group Flow

Abstract

We study Umklapp couplings and their renormalisation 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 behaviour of these couplings under renormalisation group is studied. 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.

Style : Revtex ; There are five figures, not included in this file, but very important for following the arguments of the paper. They will be provided by fax on request