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, ν=(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.