A Conformal Field Theory for the Quantum Hall Effect

TL;DR

This paper develops a conformal field theory framework for the quantum Hall effect, deriving the Laughlin wavefunction as a correlation function within this theoretical model.

Contribution

It introduces a novel CFT-based effective field theory for the quantum Hall effect, linking particle dynamics to conformal invariance and deriving the Laughlin wavefunction.

Findings

CFT describes the quantum Hall system in the large N limit when coupling constants are equal.

The effective Hamiltonian captures cyclotron motion and current interactions.

Laughlin wavefunction obtained as a correlation function of vertex operators.

Abstract

The QHE is studied in the context of a CFT. An effective field of $N$ ``spins" associated with the cyclotron motion of particles is taken as an order parameter from which an effective Hamiltonian may be defined. This effective Hamiltonian describes the COM motion of the $N$ particles (with coupling $\kappa_0$) together with a current-current interaction (of strength $\kappa_1$). Such a system gives rise to a CFT in the large $N$ limit when $\kappa_0 = \kappa_1$. The Laughlin wavefunction is derived from this CFT as an $N'$-point correlation function of winding state vertex operators.