Unconventional Phases and Phase Transitions in Electronic and Trapped Cold Atom Systems

该奖项支持理论凝聚态物理的综合研究和教育。PI旨在研究强相关电子和冷原子系统中的非常规相和相变。这项研究的动机是观察到强相互作用可以将这些系统驱动到非常规阶段，这是无法用费米液体理论等标准范式描述的。PI将在开发非常规相和相变的模型和理论的过程中承担特定的目标。它们包括：支持具有非阿贝尔统计的准粒子的分数量子霍尔相的不寻常的体积和边缘特性；支持各种类型的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；玻色子和费米子原子/分子混合形成的奇异相；以及半导体中粒子和空穴配对形成的激子态。所有这些相和相变目前都被实验学家和理论学家非常积极地研究着。本文提出的理论研究将采用各种解析和数值方法。具体方法包括玻色子化、重整化群、粒子-涡旋对偶变换、精确对角化和平均场理论的数值实现。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些非常规相的奇异性质的实验方法。该项目为研究生和博士后提供了学习先进理论技术和计算方法的教育机会。PI还将大力参与为科学界提供的各种服务，包括组织国家和国际专业会议。该奖项支持理论凝聚态物理的综合研究和教育。该项目旨在研究电子和原子在某些材料中自我组织的不寻常方式。这种组织比简单的空间组织更微妙，比如晶体中原子的周期性排列。其中一些状态是众所周知的，包括超导的原始巴丁、库珀和施里弗状态，这是一种可以导电而不耗散的物质状态。其他州是预测。PI将研究并从理论上解释在各种材料中可能检测到的这种非常规的电子和原子顺序。这项研究的中心目标是建立相关的理论模型，理解这些非常规相的性质，以及涉及它们的相变。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非常规秩序的奇异性质的实验方法。该项目为研究生和博士后提供了学习先进理论技术和计算方法的教育机会。PI还将大力参与为科学界提供的各种服务，包括组织国家和国际专业会议。

TECHNICAL SUMMARYThis award supports integrated research and education in theoretical condensed matter physics. The PI aims to investigate unconventional phases and phase transitions in strongly correlated electronic and cold atom systems. The research is motivated by the observation that strong interactions can drive these systems into unconventional phases, which cannot be described by standard paradigms like the Fermi liquid theory. The PI will undertake specific goals en route to developing models and theories of unconvetional phases and phase transitions. They include: Unusual bulk and edge properties of fractional quantum Hall phase(s) that support quasiparticles with non-Abelian statistics; cold atom systems that support various types of fractional quantum Hall phase(s) and undergo quantum phase transitions between them; exotic phases formed by mixtures of bosonic and fermionic atoms/molecules; and excitonic states formed by pairing particles and holes in semiconductors. All of these phases and phase transitions are currently being studied very actively by both experimentalists and theorists. Various analytical and numerical methods will be used in the theoretical studies proposed here. Specific methods include bosonization, renormalization group, particle-vortex duality transformation, exact diagonalization, and numerical implementation of mean-field theories. Emphasis is on calculating physical quantities that can be measured experimentally, and finding experimental methods that can reveal the exotic properties of such unconventional phases most directly.This project provides educational opportunities for graduate student and postdoctoral researchers to learn advanced theoretical techniques and computational methods. The PI will also be heavily involved in various services to the scientific community, including organizing national and international professional conferences.NONTECHNICAL SUMMARYThis award supports integrated research and education in theoretical condensed matter physics. The PI aims to investigate unusual ways in which electrons and atoms in certain materials can organize themselves. This organization is more subtle than simple spatial organization, such as the regular periodic array of atoms in a crystal. Some of these states are well known, including the original Bardeen, Cooper, and Schrieffer state for superconductivity, a state of matter that can conduct electricity without dissipation. Other states are predictions. The PI will investigate and theoretically explain such unconventional ordering of electrons and atoms in a variety of materials where it might be detected. This research involves developing pertinent theoretical models and understanding the properties of such unconventional phases, as well as phase transitions involving them, as its central goal. Emphasis is on calculating physical quantities that can be measured experimentally, and finding experimental methods that can reveal the exotic properties of unconventional order most directly.This project provides educational opportunities for graduate student and postdoctoral researchers to learn advanced theoretical techniques and computational methods. The PI will also be heavily involved in various services to the scientific community, including organizing national and international professional conferences.