On the dual topological quantum numbers filling factors

TL;DR

This paper proposes a fracton-based framework to explain the fractional quantum Hall effect, emphasizing dual topological quantum numbers and a symmetry principle linking fractal parameters, spin, and filling factors.

Contribution

It introduces a novel fracton-based model connecting fractal geometry, topological quantum numbers, and the FQHE, highlighting duality symmetry in filling factors.

Findings

FQHE occurs in pairs of dual topological quantum numbers

Fracton properties relate to fractal dimensions and spin

Duality symmetry governs the universal classes of fractons

Abstract

We consider recent experimental results [W. Pan {\it et al}, Phys. Rev. Lett. {\bf 90}, 016801 (2003)] for occurrence of the fractional quantum Hall effect-FQHE under the perspective of our formulation in terms of {\it fractons}. These objects carry rational or irrational values of spin and satisfy a {\it fractal distribution function} associated with a {\it fractal von Neumann entropy}. According to our approach the {\it FQHE occurs in pairs of dual topological quantum numbers fillings factors} and this geometrical character comes from the {\it connection betwenn the fractal parameter or Hausdorff dimension $h$ and the spin $s$ of the particles}. We suggest to the experimentalists consider our ideas and verify in fact that this phenomenon of FQHE satisfy a {\it symmetry principle} discovered by us, i.e, {\it the duality symmetry betwenn universal classes of fractons}.