c = 1 conformal field theory and the fractional quantum Hall effect

TL;DR

This paper explores how a $c=1$ conformal field theory, specifically the Gaussian model with boundary conditions, effectively describes the Laughlin states in the fractional quantum Hall effect, emphasizing the role of the chiral sector.

Contribution

It demonstrates that a $c=1$ conformal field theory with suitable boundary conditions models the Laughlin FQHE, linking conformal theory to quantum Hall phenomena.

Findings

Gaussian model with boundary conditions describes Laughlin states

Chiral sector corresponds to plateau formation

Effective theory captures key FQHE features

Abstract

We examine the application of $c=1$ conformal field theory to the description of the fractional quantum Hall effect (FQHE). It is found that the Gaussian model together with an appropriate boundary condition for the order parameter furnishes an effective theory for the Laughlin type FQHE. The plateau formation condition corresponds to taking the {\em chiral} portion of the theory.