Molecular Impurities as a Realization of Anyons on the Two-Sphere.

Studies on the experimental realization of two-dimensional anyons in terms of quasiparticles have been restricted, so far, to only anyons on the plane. It is known, however, that the geometry and topology of space can have significant effects on quantum statistics for particles moving on it. Here, we have undertaken the first step toward realizing the emerging fractional statistics for particles restricted to move on the sphere instead of on the plane.

Fermionic behavior of ideal anyons.

We prove upper and lower bounds on the ground-state energy of the ideal two-dimensional anyon gas. Our bounds are extensive in the particle number, as for fermions, and linear in the statistics parameter . The lower bounds extend to Lieb-Thirring inequalities for all anyons except bosons.

Emergence of Fractional Statistics for Tracer Particles in a Laughlin Liquid.

We consider a thought experiment where two distinct species of 2D particles in a perpendicular magnetic field interact via repulsive potentials. If the magnetic field and the interactions are strong enough, one type of particles forms a Laughlin state and the other type couples to Laughlin quasiholes. We show that, in this situation, the motion of the second type of particles is described by an effective Hamiltonian, corresponding to the magnetic gauge picture for noninteracting anyons.