Laughlin states on the sphere as representations of Uq(sl(2))

TL;DR

This paper explores the quantum algebraic structures underlying Laughlin states on a spherical geometry with a magnetic monopole, linking the deformation parameter to the particle filling ratio.

Contribution

It demonstrates that the deformation parameter in the quantum algebra corresponds to the filling ratio in Laughlin states on a sphere, providing a new algebraic perspective.

Findings

Deformation parameter relates to the filling ratio.

Quantum algebraic structures describe Laughlin states.

Spherical geometry with monopoles is analyzed.

Abstract

We discuss quantum algebraic structures of the systems of electrons or quasiparticles on a sphere of which center a magnetic monople is located on. We verify that the deformation parameter is related to the filling ratio of the particles in each case.