  Recently it was shown that anyons on the two-sphere naturally arise from a
system of molecular impurities exchanging angular momentum with a many-particle
bath (Phys. Rev. Lett. 126, 015301 (2021)). Here we further advance this
approach and rigorously demonstrate that in the experimentally realized regime
the lowest spectrum of two linear molecules immersed in superfluid helium
corresponds to the spectrum of two anyons on the sphere. We develop the
formalism within the framework of the recently experimentally observed angulon
quasiparticle.
