The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at a better fundamental understanding of the consequences of strong correlation.
Experiments on several classes of layered systems, and on nanoscale aqueous actinide complexes, call for a deeper theoretical understanding of strongly correlated electronic systems. The statistics of dynamical systems such as turbulent flows also require the accurate treatment of strong many-body correlations. The proposed research will employ a combination of systematic analytical and numerical methods to establish phase diagrams, to study charge-transfer at surfaces and in aqueous environments, and to statistically describe nonlinear systems driven out of equilibrium. Three different classes of systems will be investigated:
1. Layered materials such as the Cs2CuCl4 and organic k-(BEDT-TTF)2Cu2(CN)3 quantum antiferromagnets, and the Sr14-xCaxCu24O41 ladder materials, exhibit rich behavior characteristic of strongly correlated electronic systems. Antiferromagnetic spin order, spin liquids, gapless deconfined spinon excitations, superconductivity and pseudogap phenomena are either known to occur, or are viable possibilities. Exact diagonalization studies, Gutzwiller variational calculations, renormalization-group and density-matrix renormalization-group calculations, and multi-dimensional bosonization will be used separately, and in combination, to investigate the phase structure of models of the layered materials. The dynamical formation of a Kondo resonance in atom-surface scattering will also be investigated using a systematic truncation of the many-body Hilbert space. Close collaboration with several experimental groups is an important part of this proposed research.
2. Actinide ions in aqueous solution disproportionate into multiple oxidation states. The striking degeneracy of the reduction-oxidation potentials suggests that a higher-level organizing principle is at work. This hypothesis is reinforced by the fact that standard density-functional calculations alone are unable to reproduce the degeneracy in the redox potentials. The existence of strong electronic correlations among the 5f electrons may explain this failure. An interdisciplinary project to investigate the physics and chemistry behind actinide disproportionation will be carried out. The possibility that emergent negative-U physics leads to the degeneracy of the redox potentials will be tested by the construction and diagonalization of generalized Hubbard clusters.
3. Classical nonlinear dynamical systems such as turbulent flows often exhibit rich behaviors that defy simple explanation. A new approach based upon the Hopf functional method will be used to map the equations of motion for the statistics into a linear framework that resembles quantum mechanics. Techniques borrowed from quantum many-body theory, in particular the powerful flow-equation approach for the renormalization of Hamiltonians, will then be applied. This combined Hopf-Flow approach offers several advantages over past attempts to use renormalization-group ideas in the study of turbulence. To validate the method, comparison will be made with direct numerical simulation.
On intellectual grounds, the proposed research will push the boundaries of what can be done to ascertain emergent properties of strongly correlated systems. Gaining a better understanding of this physics is of fundamental importance. This research activity bears on 4 of the 125 outstanding scientific questions identified by Science Magazine in 2005: (1) Is there a unified theory explaining all correlated electron systems? (2) What is the pairing mechanism behind high-temperature superconductivity? (3) What is the structure of water? And (4) Can we develop a general theory of the dynamics of turbulent flows and the motion of granular materials?
The proposed work also has several broader impacts. New theoretical tools will be developed and made available to the wider community. Application to the pressing problems of safe storage of actinide nuclear wastes, and to the statistics of geophysical fluid dynamics, important for a better understanding of climate, will be made. Finally, several undergraduates, graduate students, and a postdoc will be trained in cutting-edge methods of theoretical condensed matter physics.
Non-Technical Summary: The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at a better fundamental understanding of systems containing electrons or atoms that interact strongly with each other. Strong interactions give rise to correlations in the motions of the constituent particles. In the case of electrons, the PI plans to focus on new phases of mater that can appear in layered materials and the unusual chemistry of actinides, like Neptunium and Plutonium, in water that arise as a consequence of correlations in the motion of electrons. The PI further plans to adapt and extend methods developed for the study of quantum mechanical many particle systems to develop a new approach to the problems of turbulence and fluid flow with potential applications to the study of geophysical fluid dynamics, important for a better understanding of climate.
Gaining a better understanding of this physics of strongly correlated systems of particles is of fundamental importance. This research activity bears on 4 of the 125 outstanding scientific questions identified by Science Magazine in 2005: (1) Is there a unified theory explaining all correlated electron systems? (2) What is the pairing mechanism behind high-temperature superconductivity? (3) What is the structure of water? And (4) Can we develop a general theory of the dynamics of turbulent flows and the motion of granular materials?
New theoretical tools will be developed and made available to the wider community as a direct consequence of this project. Application to the pressing problems of safe storage of actinide nuclear wastes, and to the statistics of geophysical fluid dynamics will be made. Several undergraduates, graduate students, and a postdoc will benefit from this interdisciplinary project and will be trained in cutting-edge methods of theoretical condensed matter physics.
