Renormalization group approach to Fermi Liquid Theory

TL;DR

This paper demonstrates that a one-loop renormalization group approach, considering specific scattering channels, reproduces Fermi liquid theory results and clarifies the relation between Landau parameters and RG fixed points.

Contribution

It shows how the RG approach recovers Fermi liquid theory and relates Landau parameters to the RG fixed points, extending the understanding of fermionic interactions.

Findings

RG approach recovers Fermi liquid results at one-loop order

Landau parameters linked to RG fixed points

Conditions for all-order validity specified

Abstract

We show that the renormalization group (RG) approach to interacting fermions at one-loop order recovers Fermi liquid theory results when the forward scattering zero sound (ZS) and exchange (ZS$'$) channels are both taken into account. The Landau parameters are related to the fixed point value of the ``unphysical'' limit of the forward scattering vertex. We specify the conditions under which the results obtained at one-loop order hold at all order in a loop expansion. We also emphasize the similarities between our RG approach and the diagrammatic derivation of Fermi liquid theory.