Towards a field theory of the fractional quantum Hall states

TL;DR

This paper develops a Chern-Simons field theory for the fractional quantum Hall effect, deriving wavefunctions, currents, and quasiparticle operators, and analyzing the case at filling factor 1/2 with neutral quasiparticles.

Contribution

It introduces a novel Chern-Simons framework that incorporates flux attachment and correlation holes, providing new insights into the fractional quantum Hall states.

Findings

Derived correlated wavefunctions and operators for quasiparticles.

Showed kinetic energy is replaced by interaction energy in the system.

Identified neutral quasiparticles at filling factor 1/2.

Abstract

We present a Chern-Simons theory of the fractional quantum Hall effect in which flux attachment is followed by a transformation that effectively attaches the correlation holes. We extract the correlated wavefunctions, compute the drift and cyclotron currents (due to inhomogeneous density), exhibit the Read operator, and operators that create quasi-particles and holes. We show how the bare kinetic energy can get quenched and replaced by one due to interactions. We find that for $\nu =1/2$ the low energy theory has neutral quasiparticles and give the effective hamiltonian and constraints.