Renormalization Group Approach to Low Temperature Properties of a Non-Fermi Liquid Metal

TL;DR

This paper applies a renormalization group approach to analyze the low-temperature behavior of a non-Fermi liquid metal near half-filling, emphasizing gauge invariance and composite operators.

Contribution

It extends previous RG analysis by incorporating curvature effects, composite operators, and gauge invariance to better understand non-Fermi liquid fixed points.

Findings

Derived physical consequences from RG equations for finite-size scaling.

Highlighted the importance of gauge invariance and Ward identities.

Proposed an experiment to observe characteristic non-Fermi liquid features.

Abstract

We expand upon on an earlier renormalization group analysis of a non-Fermi liquid fixed point that plausibly govers the two dimensional electron liquid in a magnetic field near filling fraction $\nu=1/2$. We give a more complete description of our somewhat unorthodox renormalization group transformation by relating both our field-theoretic approach to a direct mode elimination and our anisotropic scaling to the general problem of incorporating curvature of the Fermi surface. We derive physical consequences of the fixed point by showing how they follow from renormalization group equations for finite-size scaling, where the size may be set by the temperature or by the frequency of interest. In order fully to exploit this approach, it is necessary to take into account composite operators, including in some cases dangerous ``irrelevant'' operators. We devote special attention to gauge invariance, both as a formal requirement and in its positive role providing Ward identities constraining the renormalization of composite operators. We emphasize that new considerations arise in describing properties of the physical electrons (as opposed to the quasiparticles.) We propose an experiment which, if feasible, will allow the most characteristic feature of our results, that is