Umklapp Processes for Electrons and Their Renormalisation Group Flow

TL;DR

This paper investigates how Umklapp scattering processes influence the low-energy behavior of electrons in a 2D lattice, revealing their marginal nature under renormalisation and potential impacts on Fermi liquid properties.

Contribution

It demonstrates that nonforward Umklapp couplings are significant and remain marginal under renormalisation group flow in two-dimensional electron systems.

Findings

Umklapp couplings are substantial at high fillings.

These couplings remain marginal under RG flow.

Implications for Fermi liquid theory are discussed.

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.