New Research Directions

Computational condensed matter physics is a rapidly developing and exciting field. In part, this is due to the development of new algorithms and the large investment in cyberinfrastructure by the NSF, DOE and other funding agencies. It is also due to the interest in complex systems that are not amenable to approximate methods due to strong electronic correlations. Many important classes of materials are strongly correlated, that is, the interactions between electrons are large. Many magnets and superconductors fall into this category, including the lanthanides and actinides, heavy Fermion materials, transition metal oxides, high-temperature superconductors, manganites, ferromagnetic semiconductors,and high-density ferromagnets. Although these are materials of great technological promise, they are poorly understood due to long-ranged spin and charge correlations, competing ground states, and their complex phase diagrams. The numerical methods we have developed are ideal for study of some of these systems.

In the short term, my research will employ the numerical tools we have developed to study some of these systems. Several projects are ongoing which employ these methods to study ferromagnetic semiconductors and other correlated systems such as the cuprates and other correlated electronic materials. In GaAs doped with Mn, we are studying the effect of the strong spin-orbit interaction. It causes frustration and anisotropy. In the cuprates, we are developing a better understanding of the pairing interaction and the role of phonons in model systems, and developing (LDA+) first-principles methods to study transition metal oxides. These efforts are funded by the NSF, a DOE CMSN grant, and subcontracts through Oak-Ridge National Laboratory. I am also the PI on a new SciDAC project ($3 Million over 5 years, 9/15/06-9/14/11) to support the development of a Multi-Scale Many body formalism. The DCA treats correlations at short length scales, within the cluster, explicitly, while those at longer length scales are treated with a mean field approximation. As part of the SciDAC project, we have generalized this formalism to add a third, intermediate length scale, in which correlations are treated diagrammatically.

My long term research goal is to continue to develop and employ numerical methods to study correlated systems; however, I also plan to branch out into other areas in which a combination of analytic and numerical techniques holds promise. For example, one of my recent PhD student's thesis involved the application of information theory to bioinformatics. I am also interested in the many time scale problem which arises in numerous fields. For example, the non-covalent interactions between DNA strands, proteins, and DNA and proteins are of great fundamental importance to the interpretation of the genome, drug discovery, etc. However, here, the tremendous spread in timescales presents a fundamental challenge to simulations. I have recently shown that the DCA formalism provides a fully causal and systematic framework to construct a temporal effective medium theory in which correlations at short time scales are treated explicitly while those at longer times are treated in a mean field.