Two-dimensional abelian anyons are quasi-particles whose exchange phase differs from the standard bosonic/fermionic ones. In the magnetic gauge picture, they are represented as fermions coupled to magnetic flux tubes. For the ground state of such a system in a trapping potential, we numerically investigate a Hartree approximate model, leading to a fermionic variant of the Chern-Simons-Schrödinger system. We find that for dense systems, a semi-classical approximation yields qualitatively good results. Namely, a density functional theory of magnetic Thomas-Fermi type correctly captures the trends of our numerical results. In particular, we explore the subtle dependence of the ground state with respect to the fraction of magnetic flux units attached to particles.
Joint work with Antoine Levitt and Douglas Lundholm