My main area of interest lies in the physics of strongly correlated electronic materials which include many nanostructures, high Tc superconductors, and heavy Fermion and magnetic materials. These materials are characterized by one or more of the following phenomena: a Mott-Hubbard insulating phase, magnetism, non-Fermi liquid behavior or a very small Fermion degeneracy energy. In general, exact solutions of models of these systems are not possible, and attempts to use uncontrolled analytic techniques have met with limited success. However, in addition to the usual many-body techniques, I have developed techniques which separate the problem into strongly interacting and weakly interacting parts. The weakly interacting parts are treated with either perturbation theory or mean-field approaches, and then integrated out of the action. The remaining strongly interacting part of the action may be mapped to a small effective cluster problem which is treated with Quantum Monte Carlo (QMC) or other non-perturbative approaches. I have also developed methods used to analytically continue QMC imaginary time results to real frequencies. This allows QMC simulations to address experiments such as reflectivity, photoemission, inelastic neutron scattering and transport
