Second-quantization picture of the edge currents in the fractional quantum Hall effect

TL;DR

This paper develops a second-quantized theoretical framework for edge currents in the fractional quantum Hall effect, revealing how Laughlin wave functions naturally emerge from the quantum field description.

Contribution

It introduces a second-quantization approach to describe edge currents, connecting microscopic electron dynamics with macroscopic chiral quantum field theory.

Findings

Derivation of a chiral quantum field theory for edge currents

Emergence of Laughlin wave functions in the second-quantized framework

Insight into the microscopic origin of fractional quantum Hall states

Abstract

We study the quantum theory of two-dimensional electrons in a magnetic field and an electric field generated by a homogeneous background. The dynamics separates into a microscopic and macroscopic mode. The latter is a circular Hall current which is described by a chiral quantum field theory. It is shown how in this second quantized picture a Laughlin-type wave function emerges.