9803686 Talamantes This is an award for Research at Undergraduate Institutions (RUI). The project is a theoretical one which uses extensive numerical calculations and addresses issues related to properties of electrons and their interactions near the so-called metal-insulator transition. An important example of disordered systems with interactions between particles is that of Anderson-localized systems with Coulomb interactions. For such systems Anderson showed that a metal-insulator transition (MIT) ensues as the magnitude of disorder increases in relation to the quantum mechanical overlap energies between nearest neighbor particles. In the original discussion the effects of electron-electron interactions were neglected. Numerous studies have been made of Coulomb effects on the metallic side of the MIT. While effort has gone into how interactions affect the insulating side of the transition, this problem has been more resilient to progress. Electron-electron interactions energies on the insulating side are often of the same order as other energies of the system and, hence, cannot be neglected. Many aspects of disordered systems with electron-electron interactions are still poorly understood. This grant will focus on the question of how long-range electron-electron interactions affect the degree of electron localization on the insulating side of the MIT. The method to be used is a theoretical/computational approach which starts with electronic states corresponding to the well-localized limit. Using these states as a basis, one then computes the states as lattice spacing decreases. Those states and the energy spectrum are then analyzed by comparing various measures of the degree of delocalization for systems with and without long-range interactions. The research will investigate such questions as the effect of system size on the results, as well as that of dimensionality, density of sites, strength of the disorder, and the effect of boundary condit ions. %%% This is an award for Research at Undergraduate Institutions (RUI). The project is a theoretical one which uses extensive numerical calculations and addresses issues related to properties of electrons and their interactions near the so-called metal-insulator transition. This grant will focus on the question of how long-range electron-electron interactions affect the degree of electron localization on the insulating side of the metal-insulator transition. The method to be used is a theoretical/computational approach which starts with electronic states corresponding to the well-localized limit. Using these states as a basis, one then computes the states as lattice spacing decreases. Those states and the energy spectrum are then analyzed by comparing various measures of the degree of delocalization for systems with and without long-range interactions. The research will investigate such questions as the effect of system size on the results, as well as that of dimensionality, density of sites, strength of the disorder, and the effect of boundary conditions. ***
