Numerical work is proposed to help resolve outstanding problems in the fractionally quantized Hall states of two-dimensional electrons in strong magnetic fields. Such states are realized in semiconductor MOSFETS and hetrostructure devices which, apart from applied perspective, are valuable testing grounds for the understanding of physical phenomena in the extreme quantum limit where cooperative effects occur. In particular, the project addresses questions on: the off-diagonal long range correlations; the reversed spin excitations and their importance to even denominator rational Landau-level occupations; the approach to the classical limit of a Wigner crystal; and, the role of disorder in degradation of the fractional quantum Hall states. Also proposed is a finite-size study of planar antiferromagnets on both square and triangular lattices. The square lattice systems are realized in the oxygen-copper layers of high temperature superconductors and are deemed important to the ultimate understanding of superconducting mechanism. Detailed studies of the ground state and the excitation spectrum plus the effect and the behavior of holes in the frustrated model with next-neighbor antiferromagnetic coupling have been proposed. A parallel study of the excitation spectrum of the triangular antiferromagnet where very strong quantum fluctuation effects are also present will be carried out.
