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

该奖项支持理论凝聚态物理学的综合研究和教育。PI旨在研究强关联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，这不能用费米液体理论等标准范式来描述。PI将在开发非对称相和相变的模型和理论的过程中实现具体目标。它们包括：分数量子霍尔相位的不寻常的体积和边缘特性，支持具有非阿贝尔统计的准粒子;冷原子系统，支持各种类型的分数量子霍尔相位并在它们之间进行量子相变;由玻色子和费米子原子/分子的混合物形成的奇异相;以及由半导体中的粒子和空穴配对形成的激子态。所有这些阶段和相变目前正在非常积极地研究实验学家和理论家。在这里提出的理论研究中将使用各种分析和数值方法。具体的方法包括玻色化、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。重点是计算可以实验测量的物理量，并寻找能够最直接地揭示这种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研究人员提供了学习先进理论技术和计算方法的教育机会。PI还将积极参与科学界的各种服务，包括组织国家和国际专业会议。非技术性总结该奖项支持理论凝聚态物理的综合研究和教育。PI旨在研究某些材料中的电子和原子可以组织自己的不寻常方式。这种组织比简单的空间组织更微妙，例如晶体中原子的规则周期性排列。这些状态中的一些是众所周知的，包括最初的超导状态，库珀和施里弗状态，一种可以导电而不耗散的物质状态。其他国家都是预测。PI将研究并从理论上解释可能被检测到的各种材料中电子和原子的非常规排序。这项研究涉及开发相关的理论模型和理解这些非常规相的性质，以及涉及它们的相变，作为其中心目标。重点是计算可以实验测量的物理量，寻找最直接揭示非常规有序奇异性质的实验方法，为研究生和博士后研究人员提供学习先进理论技术和计算方法的教育机会。PI还将积极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.