(Mis-)handling gauge invariance in the theory of the quantum Hall effect III: The instanton vacuum and chiral edge physics

TL;DR

This paper develops a comprehensive effective theory for quantum Hall edge excitations using instanton vacuum concepts, linking it to chiral edge bosons, and addresses longstanding issues like disorder, interactions, and tunneling with novel non-Fermi liquid results.

Contribution

It establishes a fundamental connection between instanton vacuum methods and chiral edge physics, introducing a network model for plateau transitions and deriving non-Fermi liquid tunneling behavior.

Findings

Derived a complete effective theory of edge excitations.

Linked instanton vacuum approach to chiral edge bosons.

Predicted non-Fermi liquid tunneling behavior at integer fillings.

Abstract

The concepts of an instanton vacuum and F-invariance are used to derive a complete effective theory of massless edge excitations in the quantum Hall effect. We establish, for the first time, the fundamental relation between the instanton vacuum approach and the theory of chiral edge bosons. Two longstanding problems of smooth disorder and Coulomb interactions are addressed. We introduce a two dimensional network of chiral edge states and tunneling centers (saddlepoints) as a model for the plateau transitions. We derive a mean field theory including the Coulomb interactions and explain the recent empirical fits to transport at low temperatures. Secondly, we address the problem of electron tunneling into the quantum Hall edge. We express the problem in terms of an effective Luttinger liquid with conductance parameter (g) equal to the filling fraction (\nu) of the Landau band. Hence, even in the integral regime our results for tunneling are completely non-Fermi liquid like, in sharp contrast to the predictions of single edge theories.