Plasmons, Magnetoplasmons and the \nu = 1/2 Quantum Hall Effect

TL;DR

This paper develops a field theoretic approach to separate short-distance cyclotron physics from long-distance low-energy physics in the fractional quantum Hall effect at filling factor 1/2, leading to insights into wavefunctions and collective excitations.

Contribution

It introduces a method using field transformations to connect electron physics with flux-carrying fermions and magnetoplasmons, advancing understanding of the rac{1}{2} quantum Hall state.

Findings

Derived Jain and Rezayi-Read wavefunctions

Extended RPA analysis of Halperin, Lee, and Read

Clarified the separation of energy scales in the FQHE

Abstract

We address the problem of separating the short-distance, high-energy physics of cyclotron motion from the long- distance, low-energy physics within the Lowest Landau Level in field theoretic treatments of the Fractional Quantum Hall Effect. We illustrate our method for the case $\nu =1/2$. By a sequence of field transformations we go from electrons to fermions that carry flux tubes of thickness $l_o$ (cyclotron radius) and couple to harmonic oscillators corresponding to magnetoplasmons. The fermions keep track of the low energy physics while the oscillators describe the Landau level, cyclotron currents etc. From this starting point we are able to get Jain and Rezayi-Read wavefunctions, and many subsequent modifications of the RPA analysis of Halperin, Lee and Read.