This award was made on a 'small' category proposal submitted in response to the ITR solicitation, NSF-02-168. It supports computational and theoretical research on novel correlated electron physics arising from interactions between localized magnetic moments and itinerant electrons. The PI seeks to gain understanding of fundamental models. Through critical comparison between model results and experiments, the PI hopes to elucidate the role of correlations in heavy-fermion compounds and high-temperature superconductors. To meet these goals, the capabilities of the numerical renormalization group (NRG) technique for treating magnetic impurity problems will be significantly extended. An important open question in correlated electron physics concerns the role of zero-temperature phase transitions in accounting for the unconventional metallic states in high temperature superconductors and related materials, heavy-fermion materials, and two-dimensional electron systems. This project focuses on a novel class of quantum critical points (QCPs) at which critical fluctuations of local degrees of freedom play a crucial role. Such "local QCPs" may underlie the anomalous magnetic ordering transition found in some heavy-fermion materials, as well as the magnetic response exhibited by nonmagnetic impurities in high-temperature superconductors. The aim of the research is to develop a deeper understanding of the physics of local critical fluctuations, primarily through calculations using the NRG technique. The proposed activity has two main thrusts: 1. Extend the NRG technique so that the extended dynamical mean-field approximation can be applied to lattice problems. This will enable access to approximate solutions of the Kondo lattice model of heavy fermions that are not accessible from perturbative approaches in order to establish the existence of a local QCP in this model and to determine the physical properties near this QCP. 2. Developing parallel algorithms for NRG for distributed memory machines to enable calculations involving large basis sets. This enhanced capability will be used to investigate local QCPs in magnetic impurity models that exhibit critical local-moment fluctuations-studies of interest in their own right that will also be of value in developing theories of local criticality in lattice systems. The models will be used to calculate magnetic properties produced by doping nonmagnetic impurities into d-wave superconductors, permitting comparison with experiments on impurities in high-Tc cuprates. This work will not only yield insight into the effect of the impurities, but should also provide indirect information about the host materials. It will also result in the creation of new computational tools and their application to fundamental problems involving critical local moment fluctuations in metals and superconductors. Graduate and postdoctoral education at the frontiers of condensed matter theory will be advanced and training will be provided in advanced scientific computing. Undergraduates will be integrated into the research. Software developed as part of this project will be made available for use by other researchers. %%% This award was made on a 'small' category proposal submitted in response to the ITR solicitation, NSF-02-168. It supports computational and theoretical research on correlated electron materials. Research focuses on the consequences of interactions between localized magnetic moments and itinerant electrons and elucidating the role of electron correlations in heavy-fermion materials and high temperature superconductors. The PI will develop new computational algorithms targeted for parallel computers to implement a powerful method known as the numerical renormalization group. Resulting computer codes will be made available to the broader research community. The project will also advance graduate and postdoctoral education at the frontiers of condensed matter theory, and provide training in advanced scientific computing. Undergraduates will be integrated into the research. Software developed as part of this project will be made available for use by other researchers. ***
