Novel phases of electronic insulators and quantum Hall systems

该奖项支持材料中新型量子现象的物理学理论研究和教育。大多数固体的电子特性是在量子力学描述中被理解的，大量相互作用的电子在构成固体主体的带电原子核的背景下运动。一个重要的现代认识是，由于量子力学，固体中空间距离较远的电子的性质可以不可避免地联系在一起，这种现象称为纠缠。量子力学纠缠在确定固体的宏观性质方面起着重要作用。当电子的运动被限制在二维空间并受到强垂直磁场的作用时，就会出现一个引人注目的典型例子。PI将开发新的概念和方法来处理这些电子状态及其在实验中的识别。他还将对对称和纠缠之间的相互作用有更深的理解，这是现代量子物理学的两个核心支柱。从历史上看，这种对电子材料的基础研究产生了许多现代电子技术基础的概念。拟议的研究将有助于科学和技术知识的连续性，使未来的技术能够以基本的方式收获量子纠缠。除了研究之外，该奖项还支持培养凝聚态物理学的现代概念和方法的研究生。在可能的情况下，本科生将参与研究。PI将开设讲座，让研究生接触相关材料的现象学和相关的实验探针。他还将开设讲座，向其他科学家传达凝聚态物理的兴奋之处。该奖项支持电子绝缘体和量子霍尔系统的新量子态物理学的理论研究和教育。具体感兴趣的相是量子霍尔系统中复合费米子的液体，绝缘磁体中的量子自旋液体，以及拓扑绝缘体的强相关亲属。在过去两年中，这三个看似不同的主题出现了显著的融合。该项目将进一步发展这些联系，并利用它们进一步加深我们对每个主题的理解。具体的问题是：i)金属粒子空穴对称半填充朗道能级的微观最低朗道能级理论，ii)量子自旋液态实验的理论描述，iii)拓扑绝缘体中强相关效应的理论和实现。项目(i)是量子霍尔效应理论的基础，旨在为半填充朗道能级金属态长波有效理论的最新发展提供微观基础。项目（ii）将寻求发展量子自旋液体理论，并与许多正在进行的莫特绝缘体实验相联系，以寻找各种量子自旋液体相的证据。项目（iii）将研究强相关效应和拓扑绝缘体现象的相互作用，这是现代量子材料研究的两个基石。除了研究之外，该奖项还支持培养凝聚态物理学的现代概念和方法的研究生。在可能的情况下，本科生将参与研究。PI将开设讲座，让研究生接触相关材料的现象学和相关的实验探针。他还将开设讲座，向其他科学家传达凝聚态物理的兴奋之处。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on the physics of new kinds of quantum phenomena in materials. The electronic properties of most solids are understood within a quantum mechanical description of a large number of interacting electrons that are moving in the background of charged atom cores that form the bulk of the solid. An important modern realization is that due to quantum mechanics, the properties of spatially distant electrons in the solid can be inextricably tied together, a phenomenon called entanglement. Quantum mechanical entanglement plays a role in determining macroscopic properties of the solid. A striking and paradigmatic example occurs when the motion of electrons is restricted to two dimensions and is subjected to a strong perpendicular magnetic field.The PI will develop new concepts and methods to deal with such electronic states and their identification in experiments. He will also develop a deeper understanding of the interplay between symmetry and entanglement, which are two of the central pillars of modern quantum physics. Historically, such fundamental research on electronic materials has generated many of the concepts that underlie modern electronic technology. The proposed research will contribute to the continuum of scientific and technological knowledge enabling future technology that harvests quantum entanglement in fundamental ways.In addition to research, the award supports the training of graduate students in modern concepts and methods in condensed-matter physics. Undergraduates will be involved in the research when possible. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and the associated experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists. TECHNICAL SUMMARYThis award supports theoretical research and education on the physics of novel quantum states of electronic insulators and quantum Hall systems. Specific phases of interest are liquids of composite fermions in quantum Hall systems, quantum spin liquids in insulating magnets, and strongly correlated relatives of topological insulators. There has been a remarkable convergence of these three seemingly different topics in the last two years. The project will develop these connections further and exploit them to further our understanding of each topic. Specific questions that will be pursued are: i) a microscopic lowest-Landau-level theory of the metallic particle-hole-symmetric half-filled Landau level, ii) a theoretical description of current experiments on quantum spin liquid states, iii) theory and realization of strong correlation effects in topological insulators.Project (i) is fundamental to the theory of the quantum Hall effect and seeks to provide a microscopic foundation to recent developments on a long-wavelength effective theory for the metallic state in the half-filled Landau level. Project (ii) will seek to develop the theory of quantum spin liquids in contact with many ongoing experiments on Mott insulators that find evidence for various kinds of quantum spin-liquid phases. Project (iii) will study the interplay of strong correlation effects and topological insulator phenomena, two cornerstones of modern work on quantum materials. In addition to research, the award supports the training of graduate students in modern concepts and methods in condensed-matter physics. Undergraduates will be involved in the research when possible. The PI will develop lectures to expose graduate students to the phenomenology of correlated materials and the associated experimental probes. He will also develop lectures to convey the excitement of condensed matter physics to other scientists.