Anyonic description of low-energy physics in the fractional quantum Hall effect

The diagonalization of a Hamiltonian in the subspace spanned by many quasiparticle states has been performed. The result, compared to the full Hilbert space diagonalization, shows that the anyonic picture of the hierarchy theory provides a very accurate description of the low-energy physics of the fractional quantum Hall system. The implication of this study on the equivalence between the hierarchy theory and the composite fermion theory is discussed.