Transport, Entanglement and Topology in Correlated Many-Particle Systems

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将利用量子力学的基本物理概念和拓扑学领域的数学概念，研究被激光捕获的材料和原子中的电子如何以不同寻常和微妙的方式组织成不同寻常的物质或相状态。物质的新电子态的发现和理解有助于理解如何操纵量子力学态以实现高性能信息处理和新的电子器件技术的知识基础。PI将开发理论模型，捕捉基本的物理原理，并推进对电子非常规相位特性的理解，例如当电子被困在半导体之间的界面并暴露在垂直于界面的高磁场中时出现的相位。PI还将调查非常规阶段的转变。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顺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理论技术、材料相关特性以及使用计算建模将理论与材料特性预测联系起来的博士后。PI还将大力参与社区服务，包括组织国家和国际专业会议。此外，PI一直致力于完成现代凝聚态物理的新研究生教材。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将在强相关电子系统中研究非常规相和它们之间的相变。这项研究的动机是意识到电子之间的强相互作用可以驱动电子系统进入非常规的阶段，这是无法用费米液体理论等标准范式描述的。重点将是提出利用输运和相关方法在实验上探测非常规相的方法，以及利用纠缠和拓扑量子数在理论上对它们进行表征。具体研究领域包括：支持具有分数电荷和统计的准粒子的分数量子霍尔相的不寻常边缘特性；支持分数量子霍尔相并在其中发生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奇异相，表现出超对称性；以及相互作用系统的纠缠特性。研究的重点是相和相变，这是目前实验家和理论家正在积极研究的。研究将采用的理论方法包括：玻色子化、重整化群和粒子-涡旋对偶变换方法。重点是计算可以通过实验测量的物理量，并提出可以直接探测所提出的非常规相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理论技术、材料相关特性以及使用计算建模将理论与材料特性预测联系起来的博士后。PI还将大力参与社区服务，包括组织国家和国际专业会议。此外，PI一直致力于完成现代凝聚态物理的新研究生教材。

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.