This award supports theoretical and computational research and education that focuses on the role of correlations among particles in quantum many-body systems. The primary thrust of the research lies in the study of the Mott transition in ultracold atoms in optical lattice traps. The PI aims to extend our understanding of critical phenomena in the Bose-Hubbard Hamiltonian on a uniform lattice to the case where a spatially varying one-particle potential can locally alter the filling and compressibility. A study of the cerium volume collapse comprises a secondary thrust. The PI aims to refine his application of the dynamical mean field theory and its extensions to the cerium volume collapse, where a metal-insulator transition in 4-f orbitals is thought to play a crucial role. Quantum Monte Carlo techniques will be used for required numerical simulations. This award also supports the integration of students into research activities at graduate and undergraduate levels. The PI will continue his activities in involving students from underrepresented groups in research and in outreach to high school students. %%% This award supports theoretical and computational research and education that focuses on the role of correlations among particles in quantum many-body systems. The primary thrust of the research lies in the study of atoms at extremely low temperature that are "trapped" in spatially periodic lattices. This atomic physics system is believed to provide a useful analog for a strongly correlated electron material and some superconductors, but unlike electrons in materials, this system may be experimentally "tunable" enabling detailed exploration of different physical states with relative ease. Traditional lattice models for strongly correlated electron materials, e.g. the Hubbard model, are believed to describe these systems. Focusing on these trapped atom systems, the PI will study a transition between analogs of superconducting and insulating states in metals and explore exotic states of matter that can arise in these systems. An aim of this work is to study atomic lattice trap systems to elucidate the complex physics of superconductors and strongly correlated materials. The PI aims to refine recently developed methods for including the effects of correlations among electrons to study a kind of "metal-insulator transition" that is believed to occur in the electrons occupying 4-f shell atomic orbitals of the element cerium. Quantum Monte Carlo techniques will be used for required numerical simulations. This award also supports the integration of students into research activities at graduate and undergraduate levels. The PI will continue his activities in involving students from underrepresented groups in research and in outreach to high school students. ***
