Haldane fractional statistics in the fractional quantum Hall effect

TL;DR

This paper tests Haldane's fractional statistics model for excitations in the fractional quantum Hall effect at filling factor 1/3, finding good agreement with predictions and insights into the stability of certain fractional states.

Contribution

The study validates Haldane's fractional-Pauli principle for FQHE excitations and refines the understanding of quasiparticle energetics and state stability.

Findings

Haldane's prediction for quasiholes and quasiparticles fits well with small system results.

Modified quasiparticle statistics improve the description of FQHE excitations.

States at 4/11 and 4/13 are likely unstable based on quasiparticle interactions.

Abstract

We have tested Haldane's ``fractional-Pauli-principle'' description of excitations around the $\nu = 1/3$ state in the FQHE, using exact results for small systems of electrons. We find that Haldane's prediction $\beta = \pm 1/m$ for quasiholes and quasiparticles, respectively, describes our results well with the modification $\beta_{qp} = 2-1/3$ rather than $-1/3$. We also find that this approach enables us to better understand the {\it energetics\/} of the ``daughter'' states; in particular, we find good evidence, in terms of the effective interaction between quasiparticles, that the states $\nu = 4/11$ and 4/13 should not be stable.