Particles in non-Abelian gauge potentials - Landau problem and insertion of non-Abelian flux

TL;DR

This paper explores the effects of non-Abelian gauge potentials on charged particles, analyzing Landau levels and flux insertion, revealing the formation of spin-textures like quantum Hall Skyrmions.

Contribution

It provides a detailed analysis of Landau levels in non-Abelian fields and demonstrates how flux insertion induces spin-textures in quantum Hall states.

Findings

Landau level spectrum depends on total angular momentum J.

Adiabatic non-Abelian flux insertion creates charged spin-textures.

Formation of quantum Hall Skyrmions observed.

Abstract

We study charged spin-1/2 particles in two dimensions, subject to a perpendicular non-Abelian magnetic field. Specializing to a choice of vector potential that is spatially constant but non-Abelian, we investigate the Landau level spectrum in planar and spherical geometry, paying particular attention to the role of the total angular momentum J = L +S. After this we show that the adiabatic insertion of non-Abelian flux in a spin-polarized quantum Hall state leads to the formation of charged spin-textures, which in the simplest cases can be identified with quantum Hall Skyrmions.