Drones, quasi-spin or iso-spin? A comparison of many-body techniques for general spin

Abstract
For an effective-spin system with 2S+1 levels there are a number of possible mappings of spin onto pseudo-fermion operators. The relative merits of three of these methods are investigated by calculating to second order the dispersion relation for coupled spin-phonon modes in crystals containing S=1 effective spin impurities. The drone formalism quickly becomes intractable at higher spin values, as does the related quasi-spin formalism, in contrast with the iso-spin (or Abrikosov projection) formalism.