Finite-Size Studies of the Incompressible State of the Fractionally Quantized Hall Effect and its Excitations

Abstract

The incompressible states of interacting two-dimensional electrons in a high magnetic field has been studied by finite-size calculations in the spherical geometry. The excitation spectrum at $\frac{1}{3}$ Landau-level filling is described, and the Laughlin-Jastrow character of the Coulomb-interaction ground state is unambiguously confirmed. As the interaction is varied, a transition to a gapless compressible state is observed.