Hierarchy of plasmas for fractional quantum Hall states

Abstract

Explicit trial wave functions are proposed for the ground state at all odd-denominator rational filling factors of the lowest Landau level of a two-dimensional electron gas. An exact sum rule valid for any isotropic state in the lowest Landau level is used to justify an approximation scheme in which the hierarchy of quantum Hall states is associated with a corresponding hierarchy of classical fluids. Results are given for the energy at many rational filling factors and for the pair-correlation function at $\nu =\frac{2}{7}$.