Response Function of the Fractional Quantized Hall State on a Sphere II: Exact Diagonalization

TL;DR

This paper investigates the excitation spectra and dynamical structure factors of fractional quantum Hall states on a sphere using exact diagonalization, comparing results with a modified RPA approach, and finds good agreement at low energies.

Contribution

It provides a detailed numerical analysis of quantum Hall excitations and validates the modified RPA method against exact diagonalization results.

Findings

Good agreement between exact diagonalization and RPA at low energies

Numerical spectra match analytical predictions in the low-energy regime

Enhanced understanding of quantum Hall state excitations

Abstract

We study the excitation spectra and the dynamical structure factor of quantum Hall states in a finite size system through exact diagonalization. Comparison is made between the numerical results so obtained and the analytic results obtained from a modified RPA in the preceding companion paper. We find good agreement between the results at low energies.