Unconventional Phases and Phase Transitions in Strongly Correlated Fermionic Systems

技术综述：该奖项支持理论凝聚态物理的综合研究、教育和推广活动。这项研究研究了强关联费米子系统中的非传统相和相变。这些强相互作用可以将费米子系统推向非传统相，这是费米液体理论等标准范式无法描述的，这一观察刺激了研究。这项研究致力于开发相关的理论模型，并了解这些非常规相的性质以及涉及到它们的相变，这是本工作的中心内容。它们包括：支持非阿贝尔统计准粒子的分数量子霍尔相(S)的边态；无序和有限系统尺寸对分数量子霍尔液体拓扑相性质的影响，特别是与拓扑量子计算有关的拓扑相；一维金属中的铁磁性相和相变；不同种类的费米子与密度不平衡配对形成的非传统费米子超流体相，以及它们之间的相变。所有这些阶段和相变目前都被实验者和理论家非常积极地研究。在本文提出的理论研究中，将使用各种解析和数值方法。具体方法包括玻色化、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。重点是计算可以通过实验测量的物理量，并找到能够最直接地揭示这种非常规相的奇异性质的实验方法。该项目聘请了参与物理学研究生学习的学生研究人员。这项研究有助于他们学习理论技术，了解材料的性质，以及使用计算建模将理论与材料性质预测联系起来的经验。此外，对于参与的研究生来说，这项研究构成了导致博士学位的论文工作的基础--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。这项研究调查了某些材料中的电子如何自我组织的不寻常方式。这种组织比简单的空间组织和六个有序类型的例子更微妙，这些有序类型涉及一对电子和那里的能态，以及取决于电子旋转方向的修改。其中一些状态是众所周知的，包括最初的负责解释超导电性的BCS状态。其他国家只是猜想而已。这项研究的目的是调查并从理论上解释在已经探测到或可能探测到这种不寻常的电子有序的各种系统中。这项研究致力于发展相关的理论模型，并理解这些非常规相的性质，以及涉及到它们的相变，是这项工作的核心。重点是计算可以通过实验测量的物理量，并找到能够最直接地揭示这种非常规有序的奇异性质的实验方法。该项目聘请了参与物理学研究生学习的学生研究人员。这项研究有助于他们学习理论技术，了解材料的性质，以及使用计算建模将理论与材料性质预测联系起来的经验。此外，对于参与研究的研究生来说，这项研究构成了博士学位论文工作的基础。

TECHNICAL SUMMARY:This award supports integrated research, education and outreach activities in theoretical condensed matter physics. The research investigates unconventional phases and phase transitions in strongly correlated fermionic systems. Research is stimulated by the observation that these strong interactions can drive fermionic systems into unconventional phases, that cannot be described by standard paradigms like the Fermi liquid theory. This research undertakes developing pertinent theoretical models and understanding the properties of such unconventional phases, as well as phase transitions involving them, is the central concern of this work.The research project undertakes specific goals en route to developing the model and theory of such phases and phase transitions. They include: edge states of fractional quantum Hall phase(s) that support quasiparticles with non-Abelian statistics; effects of disorder and finite system size on the properties topological phases in fractional quantum Hall liquids, especially those related to topological quantum computation; ferromagnetic phase and phase transition in one-dimensional metals; unconventional fermionic superfluid phases formed by pairing different species of fermions with density imbalance, and phase transitions among them. 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.The project employs student researchers who are involved in graduate study in physics. The research contributes to their education in learning the theoretical techniques and understanding the properties of the materials and experience in the use of computational modeling to connect theory to prediction of materials properties. In addition, for the graduate students involved, the research forms the basis for dissertation work leading to the Ph.D.NON-TECHNICAL SUMMARY:This award supports integrated research, education and outreach activities in theoretical condensed matter physics. The research investigates unusual ways in which electrons in certain materials can organized themselves. This organization is more subtle than simple spatial organization and half dozen examples of types of orderings involving pair of electrons and there energy states as well as modifications that depend upon the directions in which the electrons spin. Some of these states are well know, including the original BCS state responsible for explaining superconductivity. Other states are merely conjectured. It is the purpose of the research to investigate and theoretically explain such unusual orderings of electrons in the variety of systems where this has been detected or where it might be detected. This research undertakes developing pertinent theoretical models and understanding the properties of such unconventional phases, as well as phase transitions involving them, is the central concern of this work. Emphasis 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.The project employs student researchers who are involved in graduate study in physics. The research contributes to their education in learning the theoretical techniques and understanding the properties of the materials and experience in the use of computational modeling to connect theory to prediction of materials properties. In addition, for the graduate students involved, the research forms the basis for dissertation work leading to the Ph.D.