a New Method to Study Disordered Systems with Interactions

A computer simulation method which yields the ground state and low energy excited states of a system of interacting localized particles in disordered media is described. The method is applied to electrons in Anderson localized systems, when Coulomb interactions are important. Long standing controversies as to whether one electron excitations or correlated many electron excitations are important to determine the low temperature properties are addressed. The nature of low lying energy excitations is investigated. Results show that they are mainly of many electron cascade type and that successive correlations between them are important. Three kinds of relaxations are studied; energy, dielectric and relaxation due to addition or subtraction of a particle to the system. In energy relaxation the system is allowed to relax from an excited state by fastest transitions. The relaxation times of such transitions become very long as the energy is lowered indicating that the system can have a glassy property. In dielectric relaxation the electric field is applied to the ground state of the system and then the system is relaxed from the resulting excited state. The dipole moments of the transitions are calculated. The polarizability of a noninteracting and interacting systems are compared. Coulomb interaction is found to decrease the polarizability. In third kind of relaxation, in accordance with definition of single particle density of states, a particle is added or deleted from the system and then the system is allowed to relax. The relaxation times indicate that dc conductivity cannot be calculated from the single particle density of states. Finally, the system density of states and the specific heat for interacting and noninteracting systems were compared. The density of states for the interacting system rises faster than that of the noninteracting one. A region of depletion at low energies is observed for the density of states of the interacting system. The specific heat of the noninteracting system changes linearly with temperature in accordance with theoretical prediction. The interacting system shows rather strong mezoscopic effects, but there is distinct indication that the specific heat is a superlinear function of temperature. ftn*Supported in part by the San Diego Supercomputing Center; Supported in part by the Illinois Supercomputing Center.