Composite-Fermion Picture for the Spin-Wave Excitation in the fractional quantum Hall system

TL;DR

This paper demonstrates that the composite-fermion mean-field approach accurately describes spin-wave excitations in fractional quantum Hall systems at certain wavelengths, extending the composite picture to excited states and providing insights into spin stiffness.

Contribution

It shows that the composite-fermion mean-field approximation effectively models spin-wave excitations beyond the ground state in fractional quantum Hall liquids.

Findings

Accurate description of spin-wave modes for wavelengths exceeding the magnetic length.

Extension of the composite-fermion picture to excited states.

Quantitative estimation of spin stiffness from exchange interactions.

Abstract

Spin-wave excitation mode from the spin-polarized ground state in the fractional quantum Hall liquid with odd fractions ($\nu=1/3,1/5$) numerically obtained by the exact diagonalization of finite systems is shown to be accurately described, for wavelengths exceeding the magnetic length, in terms of the composite-fermion mean-field approximation for the spin-wave (magnon) theory formulated in the spherical geometry. This indicates that the composite picture extends to excited states, and also provides the spin stiffness in terms of peculiar exchange interactions.