This renewal award for Research at Undergraduate Institutions is for continued research on the fractional quantum Hall effect. Numerical work is proposed to investigate outstanding problems in the fractionally quantized Hall effect which is observed in a two- dimensional electron gas subject to a transverse magnetic field. The electron layer is formed at the semiconductor interface of a high quality Gallium-Arsenide heterostructure device. The recent availability of very high mobility samples offers a unique opportunity to probe strongly correlated systems in the extreme quantum mechanical limit, where collective phenomena occur. In addition, the more recent optical measurements of the quantum Hall states have provided another dimension in experimental probes of the quantum Hall effect. The proposed research addresses the nature of half-integral and hierarchy states of the fractional quantum Hall effect as well as the physical conditions which stabilize them. Additional areas of research include understanding edge states; the quantum fluid to classical Wigner crystal cross- over; optical signature of quantum Hall states; and, the possibility of fractional quantum Hall effect in a two-dimensional electron-hole fluid. Also proposed is a finite-size numerical study of a model Hamiltonian for which the Kalmeyer-Laughlin chiral spin fluid ground state is exact. Chiral spin fluids are similar to quantum Hall states and support fractional statistics (semion) excitations. %%% The quantum Hall effect is due to a unique state of matter - a two- dimensional electron fluid. The cooperative behavior of electrons in two-dimensions is markedly different from their behavior in the more familiar three-dimensions. The proposed research will use numerical and analytical techniques to study a number of properties of this strange two-dimensional system which are of current interest. Besides providing insight into the underlying physics of this strange state of matter, the results may also be of interest in device fabrication and for high temperature superconductivity.
