Metal-Insulator Transitions in Correlated Quantum Systems

该奖项支持专注于量子多体系统中粒子之间的关联作用的理论和计算研究和教育。研究的重点在于研究光学晶格陷阱中超冷原子的Mott跃迁。PI的目的是将我们对均匀晶格上玻色-哈密顿量中的临界现象的理解扩展到空间变化的单粒子势可以局部改变填充和可压缩性的情况。对Ce体积崩塌的研究包括一个次要推力。PI的目的是改进他对动力学平均场理论的应用及其对Ce3+体积崩塌的扩展，其中4-f轨道上的金属-绝缘体转变被认为起着关键作用。量子蒙特卡罗技术将用于所需的数值模拟。该奖项还支持学生参与研究生和本科生的研究活动。国际学生联合会将继续他的活动，让代表人数不足的群体的学生参与研究和接触高中生。该奖项支持专注于量子多体系统中粒子之间的关联作用的理论和计算研究和教育。这项研究的主要目的在于研究在极低温度下被“囚禁”在空间周期晶格中的原子。这个原子物理系统被认为为强相关的电子材料和一些超导体提供了一个有用的模拟，但与材料中的电子不同，这个系统可能在实验上是“可调的”，能够相对容易地详细探索不同的物理状态。传统的强关联电子材料晶格模型，如Hubbard模型，被认为可以描述这些体系。围绕这些被捕获的原子系统，PI将研究金属中超导态和绝缘态的类似物之间的转变，并探索这些系统中可能出现的物质的奇异状态。这项工作的目的是研究原子晶格陷阱系统，以阐明超导体和强关联材料的复杂物理。PI的目的是改进最近开发的方法，以包括电子之间的关联效应，以研究一种被认为发生在占据元素Ce的4-f壳层原子轨道的电子中的“金属-绝缘体转变”。量子蒙特卡罗技术将用于所需的数值模拟。该奖项还支持学生参与研究生和本科生的研究活动。国际学生联合会将继续开展活动，让代表人数不足的群体的学生参与研究和接触高中生。*

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.***