Hund's Rule for Monopole Harmonics, or Why the Composite Fermion Picture Works

TL;DR

This paper explains why the composite fermion model accurately predicts fractional quantum Hall states by relating it to a Hund's rule analogy for monopole harmonics, supported by numerical comparisons.

Contribution

It introduces a Hund's rule analogy for monopole harmonics to justify the success of the mean field composite fermion picture in quantum Hall systems.

Findings

The composite fermion approximation aligns with a Hund's rule for monopole harmonics.

Numerical calculations support the plausibility of this Hund's rule analogy.

The mean field composite fermion picture is justified through this new perspective.

Abstract

The success of the mean field composite Fermion (MFCF) picture in predicting the lowest energy band of angular momentum multiplets in fractional quantum Hall systems cannot be found in a cancellation between the Coulomb and Chern--Simons interactions beyond the mean field, due to their totally different energy scales. We show that the MFCF approximation can be regarded as a kind of semi-empirical Hund's rule for monopole harmonics. The plausibility of the rule is easily established, but rigorous proof relies on comparison with detailed numerical calculations.