Hausdorff dimension and filling factor

TL;DR

This paper introduces a new hierarchy scheme for the filling factor in the Fractional Quantum Hall Effect, using Hausdorff dimension to classify fractional spin particles based on their collective excitation statistics.

Contribution

It proposes a novel classification method for fractional quantum Hall states using Hausdorff dimension as a parameter for fractional spin particles.

Findings

Hausdorff dimension $h$ effectively classifies fractional excitations.

The scheme links $h$ to the homotopy class of collective excitations.

Provides a new perspective on the statistical properties of FQHE particles.

Abstract

We propose a new hierarchy scheme for the filling factor, a parameter which characterizes the occurrence of the Fractional Quantum Hall Effect (FQHE). We consider the Hausdorff dimension, $h$, as a parameter for classifying fractional spin particles, such that, it is written in terms of the statistics of the collective excitations. The number $h$ classifies these excitations with different statistics in terms of its homotopy class.