TEST OF THE HIERARCHICAL THEORY FOR THE FRACTIONAL QUANTUM HALL-EFFECT

In the hierarchical theory of the fractional quantum Hall effect, the low-energy behavior of a daughter state in the next level of the hiera rchy is described by an interacting system of quasiparticles of the pa rent state. Taking the filled lowest Landau level as the parent state, we examine analytically the quantitative consequences of this approac h for electrons interacting via a pseudopotential interaction. It is s hown that the ground-state energy per particle in the daughter state a t a filling factor 2/3 is exactly equal to that of a system of quasiho les in the parent state with half filling, precisely as predicted by t he hierarchical approach. This is achieved with only up to two-particl e interactions in the effective Hamiltonian for the quasiholes. Their single-particle energy and two-particle interaction are derived. The r esults are generalized to the other filling factors attainable from th e filled Landau level.