(Mis-)handling gauge invariance in the theory of the quantum Hall effect II: Perturbative results

TL;DR

This paper investigates the role of gauge invariance in the quantum Hall effect, performing a detailed renormalization group analysis to understand the infrared behavior and scaling near the metal-insulator transition.

Contribution

It provides a two-loop renormalization analysis of the Finkelstein action in 2+2ε dimensions, establishing renormalizability and elucidating gauge-invariant quantities' behavior.

Findings

Renormalizability of the Finkelstein action to two loops.

Explicit scaling functions for conductivity and specific heat.

Identification of a Coulomb gap in the quasiparticle density of states near the transition.

Abstract

The concept of F-invariance, which previously arose in our analysis of the integral and half-integral quantum Hall effects, is studied in 2+2\epsilon spatial dimensions. We report the results of a detailed renormalization group analysis and establish the renormalizability of the (Finkelstein) action to two loop order. We show that the infrared behavior of the theory can be extracted from gauge invariant (F-invariant) quantities only. For these quantities (conductivity, specific heat) we derive explicit scaling functions. We identify a bosonic quasiparticle density of states which develops a Coulomb gap as one approaches the metal-insulator transition from the metallic side. We discuss the consequences of F-invariance for the strong coupling, insulating regime.