Hierarchical classification of fractional quantum Hall states

Abstract

We study the hierarchy of states proposed as a generalization of Laughlin's theory of the fractional quantum Hall effect at filling fractions of the lowest Landau level, \ensuremath{\nu}=(1/3,2)/7, (2/5, 3)/7. Our studies confirm the general validity of the hierarchy. We estimate the ground- and excited-state energies at the various filling fractions, and the ``size'' and ``shape'' of the fractionally charged excitations. The gap energies are substantially larger than would be expected if one considered the fractionally charged excitations to be point charges.