Spin-Hall effect with quantum group symmetry

TL;DR

This paper models the spin-Hall effect on a noncommutative 4-sphere with quantum group symmetry, revealing integer and fractional excitations through explicit Hamiltonian diagonalization.

Contribution

It introduces a novel noncommutative geometric model of the spin-Hall effect with quantum group invariance, including explicit solutions and excitation analysis.

Findings

Explicit diagonalization of the Hamiltonian

Existence of integer and fractional excitations

Extension to higher-dimensional noncommutative spaces

Abstract

We construct a model of spin-Hall effect on a noncommutative 4 sphere with isospin degrees of freedom (coming from a noncommutative instanton) and invariance under a quantum orthogonal group. The corresponding representation theory allows to explicitly diagonalize the Hamiltonian and construct the ground state; there are both integer and fractional excitations. Similar models exist on higher dimensional noncommutative spheres and noncommutative projective spaces.