Transport, Entanglement and Topology in Correlated Many-Particle Systems

非技术总结该奖项支持理论凝聚态物理学的综合研究，教育和推广活动。PI将研究不寻常和微妙的方式，其中被激光捕获的材料和原子中的电子可以使用量子力学的基本物理概念和拓扑学领域的数学概念将自己组织成非常规的物质或相态。发现和理解物质的新电子态有助于建立知识基础，使人们能够理解如何操纵量子力学态，以实现高性能的信息处理和新的电子器件技术。PI将开发理论模型，以捕捉基本的物理原理，并促进对电子非常规相性质的理解，例如当电子在半导体之间的界面处被捕获并暴露于垂直于界面的高磁场时出现的那些。PI还将研究非常规相之间的转化。该研究的重点是计算可以通过实验测量的物理量，并找到可以最直接地揭示这种非常规有序的奇异性质的实验方法。该项目有助于培养物理学研究生和博士后研究员的理论技术，材料的相关性质，以及使用计算模型将理论与材料性能的预测联系起来。PI还将积极参与社区服务，包括组织国家和国际专业会议。此外，PI一直致力于完成一本关于现代凝聚态物理的新研究生教科书。技术总结该奖项支持理论凝聚态物理的综合研究，教育和推广活动。PI将研究强关联电子系统中的非常规相和它们之间的相变。这项研究的动机是认识到电子之间的强相互作用可以将电子系统驱动到非常规阶段，这不能用费米液体理论等标准范式来描述。重点将是提出方法来探测非常规阶段实验上使用运输和相关的方法，并在理论上表征他们使用纠缠和拓扑量子数。具体的研究领域包括：不寻常的分数量子霍尔相位的边缘特性，支持准粒子的分数电荷和统计;支持分数量子霍尔相并在它们之间经历量子相变的冷原子系统;由玻色子和费米子原子或分子的混合物形成的表现出超对称性的奇异相;和相互作用系统的纠缠特性。该研究的重点是阶段和相变，目前正在积极研究的实验学家和理论家。理论方法，将用于进行研究包括：玻色化，重整化群，和粒子涡对偶变换方法。重点是计算可以实验测量的物理量，并提出可以直接探测非常规相的奇异性质的实验方法。本项目有助于培养物理学研究生和博士后研究员的理论技术，材料的相关性质，以及使用计算建模将理论与材料性质预测联系起来。PI还将积极参与社区服务，包括组织国家和国际专业会议。此外，PI一直致力于完成一本关于现代凝聚态物理的新研究生教科书。

NON-TECHNICAL SUMMARYThis award supports integrated research, education and outreach activities in theoretical condensed matter physics. The PI will investigate unusual and subtle ways in which electrons in materials and atoms trapped by laser light can organize themselves into unconventional states of matter or phases using fundamental physical concepts from quantum mechanics and mathematical concepts from the field of topology. The discovery and understanding of new electronic states of matter contribute to the base of knowledge that enables the understanding of how to manipulation quantum mechanical states to achieve high performance information processing and new electronic device technologies.The PI will develop theoretical models that capture the essential physical principles and advance understanding of the properties unconventional phases of electrons, such as those that appear when electrons are trapped at the interface between semiconductors and exposed to a high magnetic field perpendicular to the interface. The PI will also investigate transformations among unconventional phases. The emphasis of the research is on calculating physical quantities that can be measured experimentally, and finding experimental methods that can reveal the exotic properties of such unconventional orderings most directly.This project contributes to educating graduate students in physics and a postdoctoral fellow in theoretical techniques, associated properties of materials, and in the use of computational modeling to connect theory to the prediction of materials properties. The PI will also be heavily involved in community service, including organizing national and international professional conferences. In addition the PI has been working to complete a new graduate textbook on Modern Condensed Matter Physics.TECHNICAL SUMMARYThis award supports integrated research, education and outreach activities in theoretical condensed matter physics. The PI will investigate unconventional phases and phase transitions among them in strongly correlated electronic systems. The research is motivated by the realization that strong interactions among electrons can drive electronic systems into unconventional phases, which cannot be described by standard paradigms like the Fermi liquid theory. Emphasis will be on proposing ways to probe unconventional phases experimentally using transport and related methods, and on characterizing them theoretically using entanglement and topological quantum numbers.Specific areas of investigation include: Unusual edge properties of fractional quantum Hall phases that support quasiparticles with fractional charge and statistics; cold atom systems that support fractional quantum Hall phases, and undergo quantum phase transitions among them; exotic phases formed by mixtures of bosonic and fermionic atoms or molecules that exhibit supersymmetry; and entanglement properties of interacting systems. The research is focused on phases and phase transitions that are currently under active study by experimentalists and theorists. Theoretical methods that will be used in carrying out the research include: bosonization, renormalization group, and particle-vortex duality transformation methods. The emphasis is to calculate physical quantities that can be measured experimentally, and to propose experimental methods that can directly probe the exotic properties of proposed unconventional phases.This project contributes to educating graduate students in physics and a postdoctoral fellow in theoretical techniques, associated properties of materials, and in the use of computational modeling to connect theory to the prediction of materials properties. The PI will also be heavily involved in community service, including organizing national and international professional conferences. In addition the PI has been working to complete a new graduate textbook on Modern Condensed Matter Physics.