Forward Scattering Approximation and Bosonization in Integer Quantum Hall Systems

TL;DR

This paper develops a model and method to analyze integer quantum Hall systems by mapping them into interacting one-dimensional gases, employing bosonization and forward scattering approximations to study their collective excitations and spectral functions.

Contribution

It introduces a novel approach using Landau level bosonization and forward scattering approximation to analyze IQH systems, revealing non-normal strongly correlated behaviors.

Findings

Dispersion relations for collective excitations derived

Single particle spectral functions show spin-charge splitting

Behavior consistent with Tomonaga-Luttinger model evidence

Abstract

In this work we present a model and a method to study integer quantum Hall (IQH) systems. Making use of the Landau levels structure we divide these two dimensional systems into a set of interacting one dimensional gases, one for each guiding center. We show that the so-called strong field approximation, used by Kallin and Halperin and by MacDonald, is equivalent, in first order, to a forward scattering approximation and analyze the IQH systems within this approximation. Using an appropriate variation of the Landau level bosonization method we obtain the dispersion relations for the collective excitations and the single particle spectral functions. These results evidence a behavior typical of non-normal strongly correlated systems, including the spin-charge splitting of the single particle spectral function. We discuss the origin of this behavior in the light of the Tomonaga-Luttinger model and the bosonization of two dimensional electron gases.