Nonanalyticities in a Strongly Correlated Fermi Liquid: Corrections to Scaling at the Fermi-Liquid Fixed Point

TL;DR

This paper employs scaling and renormalization-group methods to analyze nonanalytic behaviors in a Fermi liquid, confirming the exactness of previously derived exponents as leading corrections at the Fermi-liquid fixed point.

Contribution

It introduces a scaling hypothesis derived from effective field theory that confirms the exactness of nonanalyticity exponents in Fermi liquids.

Findings

Nonanalyticities in density of states and susceptibilities are confirmed.

Scaling exponents are shown to be exact as leading corrections.

Absence of nonanalytic terms in density susceptibility is discussed.

Abstract

We use scaling and renormalization-group techniques to analyze the leading nonanalyticities in a Fermi liquid. We show that a physically motivated scaling hypothesis reproduce the results known from perturbation theory for the density of states, the density-of-states fluctuations, the specific heat, the spin susceptibility, and the nematic magnetic susceptibility. We also discuss the absence of nonanalytic terms in the density susceptibility. We then use a recent effective field theory for clean electron systems to derive the scaling hypothesis by means of renormalization-group techniques. This shows that the exponents (although not the prefactors) of the nonanalyticities that were previously derived by means of perturbative techniques are indeed exact, and can be understood as the leading corrections to scaling at the stable Fermi-liquid fixed point.