We show that the introduction of a more general closed-shell operator allows one to extend Laughlin's wave function to account for the richer hierarchies $(1/3,2/5,3/7\dots ;1/5,2/9,3/13,\dots ,\mathrm{etc}.\mathrm{})$ found experimentally. The construction identifies the special hierarchy states with condensates of correlated electron clusters. This clustering implies a single-particle algebra within the first Landau level (LL) identical to that of multiply filled LLs in the integer quantum Hall effect. The end result is a simple generalized wave function that reproduces the results of both Laughlin and Jain, without reference to higher LLs or projection.

• Received 18 October 1995

DOI:https://doi.org/10.1103/PhysRevLett.77.1568