Toward a Conformal Field Theory for the Quantum Hall Effect

TL;DR

This paper proposes an effective Hamiltonian modeled as a conformal field theory to better understand the quantum Hall effect, introducing an order parameter linked to collective particle behavior or spin fields.

Contribution

It introduces a novel Hamiltonian incorporating current-current interactions that aligns with conformal field theory in the large N limit for quantum Hall systems.

Findings

Hamiltonian includes current-current interactions.

Order parameter connects collective particle and spin descriptions.

Framework aligns with conformal field theory principles.

Abstract

An effective Hamiltonian for the study of the quantum Hall effect is proposed. This Hamiltonian, which includes a ``current-current" interaction has the form of a Hamiltonian for a conformal field theory in the large $N$ limit. An order parameter is constructed from which the Hamiltonian may be derived. This order parameter may be viewed as either a collective coordinate for a system of $N$ charged particles in a strong magnetic field; or as a field of spins associated with the cyclotron motion of these particles.