Duality and anyonic excitations

TL;DR

This paper explores a duality between classes of anyonic excitations in the fractional quantum Hall effect, linking their properties through Hausdorff dimensions and suggesting a connection to conformal invariance.

Contribution

It introduces a duality concept between anyonic classes based on Hausdorff dimension and relates this to observed filling factors in FQHE systems.

Findings

Confirmation of the relation between filling factors and classes of anyonic excitations.

Identification of dual pairs of filling factors linked by the duality.

Implication of conformal invariance in the exchange of dual pairs.

Abstract

We consider anyonic excitations classified into equivalence classes labeled by Hausdorff dimension, $h$ and introduce the concept of duality between such classes, defined by $\tilde{h}=3-h$. In this way, we confirm that the filling factors for which the Fractional Quantum Hall Effect (FQHE) were observed just appears into these classes and the duality in case is between quasihole and quaasiparticle excitations for these FQHE systems.Exchanges of dual pairs $(\nu,\tilde{\nu})$, suggests conformal invariance.