Unconventional Phases and Phase Transitions in Strongly Correlated Fermionic Systems

强相关费米子系统中的非常规相和相变

• 批准号: 0704133
• 负责人: Kun Yang
• 金额: $ 25.5万
• 依托单位: Florida State University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2007
• 资助国家: 美国
• 起止时间: 2007-12-15 至 2011-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0704133&HistoricalAwards=false
• 关键词: Unconventional; Phases; Phase; Transitions; Strongly

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.

技术摘要：该奖项支持理论凝聚态物理领域的综合研究、教育和推广活动。该研究研究了强相关费米子系统中的非常规相和相变。这些强相互作用可以驱动费米子系统进入非常规相，而这种相无法用费米液体理论等标准范式来描述，这一观察结果刺激了研究。这项研究致力于开发相关的理论模型，并了解此类非常规相的性质以及涉及它们的相变，是这项工作的核心关注点。该研究项目在开发此类相和相变的模型和理论的过程中承担了特定的目标。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边缘态；无序和有限系统尺寸对分数量子霍尔液体拓扑相特性的影响，特别是与拓扑量子计算相关的影响；一维金属中的铁磁相和相变；通过密度不平衡的不同种类的费米子配对形成的非常规费米子超流体相，以及它们之间的相变。目前，实验学家和理论学家正在非常积极地研究所有这些相和相变。这里提出的理论研究将使用各种分析和数值方法。具体方法包括玻色子化、重正化群、粒子涡对偶变换、精确对角化以及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此类非常规相的奇异特性的实验方法。该项目雇用了参与物理学研究生学习的学生研究人员。 该研究有助于他们学习理论技术和理解材料特性以及使用计算模型将理论与材料特性预测联系起来的经验。此外，对于参与的研究生来说，该研究构成了获得博士学位的论文工作的基础。非技术摘要：该奖项支持理论凝聚态物理领域的综合研究、教育和推广活动。该研究调查了某些材料中电子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，并且有六个涉及电子对和能量状态的排序类型示例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，包括负责解释超导性的原始 BCS 状态。其他状态只是推测。这项研究的目的是调查并从理论上解释在已检测到或可能检测到电子的各种系统中这种不寻常的电子排序。这项研究的重点是开发相关的理论模型并了解此类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这种非常规排序的奇异特性的实验方法。该项目雇用了参与物理学研究生学习的学生研究人员。 该研究有助于他们学习理论技术和理解材料特性以及使用计算模型将理论与材料特性预测联系起来的经验。此外，对于所涉及的研究生来说，该研究构成了获得博士学位的论文工作的基础。