Model Wavefunctions for the Collective Modes and the Magneto-roton Theory of the Fractional Quantum Hall Effect

TL;DR

This paper develops model wavefunctions for collective excitations in fractional quantum Hall systems, accurately capturing their properties and extending understanding of the magneto-roton spectrum.

Contribution

It introduces a novel construction of wavefunctions using symmetric polynomials characterized by root partitions and squeezed bases, aligning well with numerical results.

Findings

Wavefunctions match exact diagonalization results

Model reduces to single-mode approximation at long wavelengths

Accurate at energies above roton pair continuum

Abstract

We construct model wavefunctions for the collective modes of fractional quantum Hall systems. The wavefunctions are expressed in terms of symmetric polynomials characterized by a root partition and a "squeezed" basis, and show excellent agreement with exact diagonalization results for finite systems. In the long wavelength limit, the model wavefunctions reduce to those predicted by the single-mode approximation, and remain accurate at energies above the continuum of roton pairs.