``Fermi Liquid'' Shell Model Approach to Composite Fermion Excitation Spectra in Fractional Quantum Hall States

TL;DR

This paper develops a Fermi liquid shell model approach to analyze composite fermion excitations in fractional quantum Hall states, providing a new confirmation of the composite fermion picture through spectral calculations.

Contribution

It introduces a shell model method to determine quasiparticle energies and interactions, extending to multi-quasiparticle spectra in fractional quantum Hall systems.

Findings

Qualitative agreement with numerical spectra

Confirmation of the composite fermion model

New insights into quasiparticle interactions

Abstract

Numerical results for the energy spectra of $N$ electrons on a spherical surface are used as input data to determine the quasiparticle energies and the pairwise ``Fermi liquid'' interactions of composite Fermion (CF) excitations in fractional quantum Hall systems. The quasiparticle energies and their interactions are then used to determine the energy spectra, $E$ vs total angular momentum $L$, of states containing more than two quasiparticles. The qualitative agreement with the numerical results gives a remarkable new confirmation of the CF picture.