My main area of interest lies in the physics of strongly correlated electronic materials which include high temperature superconductors, heavy Fermion and magnetic materials as well as lower dimensional nanoscale systems. These materials are characterized by one or more of the following phenomena: a Mott-Hubbard insulating phase, magnetism, non Fermi liquid behavior, unconventional superconductivity, 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 numerical techniques which combine quantum Monte Carlo (QMC) with self-consistent and perturbative schemes as a more reliable approach to the study of the dynamical properties of these systems. In this way, the computationally intensive QMC is used only for the non-perturbative part of the problem, allowing for a more accurate study in the thermodynamic limit by the elimination of finite size-errors common to Monte Carlo results.
Below I describe a few examples of my recent and ongoing work. If you are viewing this on line, then some relevant papers are linked in blue, for a more complete list see the publication list in my vita http://www.phys.lsu.edu/jarrell/vit/node8.html, .