Numerical study of hierarchical quantum Hall edge states in the disk geometry

We present a detailed analysis of the exact numerical spectrum of up to ten interacting electrons in the first Landau level on the disk geometry. We s tudy the edge excitations of the hierarchical plateaus and check the predic tions of two relevant conformal field theories: the multicomponent Abelian theory and the W1+infinity minimal theory of the incompressible fluids. We introduce two criteria for identifying the edge excitations within the low- lying states: the plot of their density profiles and the study of their ove rlaps with the Jain wave functions in a meaningful basis. We find that the exact bulk and edge excitations are very well reproduced by the Jain states ; these, in turn, can be described by the multicomponent Abelian conformal theory. Most notably, we observe that the edge excitations form subfamilies of the low-lying states with a definite pattern, which is explained by the W1+infinity minimal conformal theory. Actually, the two conformal theories are related by a projection mechanism whose effects are observed in the sp ectrum. Therefore, the edge excitations of the hierarchical Hall states are consistently described by the W1+infinity minimal theory, within the finit e-size limitations. [S0163-1829(98)02844-6].