Large-N Collective Field Theory Applied to Anyons in Magnetic Fields

TL;DR

This paper develops a large-N collective field theory framework for anyons in magnetic fields, reproducing Landau levels and analyzing collective excitations for various statistical parameters.

Contribution

It introduces a novel large-N collective field formalism for anyons in magnetic fields, applicable to arbitrary two-body interactions and reproducing key quantum Hall features.

Findings

Reproduces Landau levels within the collective field approach

Derives dispersion relations for collective modes of anyons

Applicable to arbitrary statistical parameters and interactions

Abstract

We present a large-$N$ collective field formalism for anyons in external magnetic fields interacting with arbitrary two-body potential. We discuss how the Landau level is reproduced in our framework. We apply it to the soluble model for anyons proposed by Girvin et al., and obtain the dispersion relation of collective modes for arbitrary statistical parameters.