The Fermi Liquid as a Renormalization Group Fixed Point: the Role of Interference in the Landau Channel

TL;DR

This paper uses a finite-temperature renormalization-group approach to analyze Fermi liquids, revealing that interference effects invalidate traditional ladder approximations and lead to temperature-dependent anomalies in scattering properties.

Contribution

It introduces a RG-based method to calculate Fermi liquid parameters, accounting for interference effects that challenge classic derivations.

Findings

Interference invalidates ladder approximation near zero angle.

Temperature-dependent anomalies appear in Landau function.

Amplitude sum rule is not valid in this RG framework.

Abstract

We apply the finite-temperature renormalization-group (RG) to a model based on an effective action with a short-range repulsive interaction and a rotation invariant Fermi surface. The basic quantities of Fermi liquid theory, the Landau function and the scattering vertex, are calculated as fixed points of the RG flow in terms of the effective action's interaction function. The classic derivations of Fermi liquid theory, which apply the Bethe-Salpeter equation and amount to summing direct particle-hole ladder diagrams, neglect the zero-angle singularity in the exchange particle-hole loop. As a consequence, the antisymmetry of the forward scattering vertex is not guaranteed and the amplitude sum rule must be imposed by hand on the components of the Landau function. We show that the strong interference of the direct and exchange processes of particle-hole scattering near zero angle invalidates the ladder approximation in this region, resulting in temperature-dependent narrow-angle anomalies in the Landau function and scattering vertex. In this RG approach the Pauli principle is automatically satisfied. The consequences of the RG corrections on Fermi liquid theory are discussed. In particular, we show that the amplitude sum rule is not valid.