Effective theories of the fractional quantum Hall effect: Hierarchy construction

The effective theories for the hierarchical fractional quantum Hall effect (FQHE) are proposed. We obtain the quantum numbers of the quasiparticles and the structure of the edge excitations for the general hierarchical FQHE state. It is shown that at the filling fractions ν=k/(2km±1) the Jain states and the hierarchical FQHE states give rise to the same quasiparticles and edge excitations and have the same effective theories (in the dual form). This suggests that these FQHE states are equivalent despite having been obtained from two different schemes.