Theories of Metals with Correlated Electrons

该奖项支持理论研究和教育，以调查量子材料中出现的不寻常金属状态，以及由这些“奇怪金属”产生的电子组成的物质的有趣状态。在铜或银等常见的金属中，导电是通过电子液体通过原子晶体的运动发生的，每个电子的量子运动在很大程度上独立于其他电子。然而，在许多现代量子材料中，特别是在表现出高温超导性的铜化合物中，电子的运动与其他电子的运动是相关的。这种关联是一种微妙的非局域量子变化，通常被称为量子纠缠，其中对一个电子的观察可以确定其他分离良好的电子的状态。在这个项目中，PI将专注于研究和分类具有复杂长程量子纠缠的电子状态。了解这种金属状态是预测高温超导的临界温度所必需的，因为这种“奇怪”的金属在降低温度时就会出现超导性。当温度通过超导转变温度降低时，超导体表现出无电阻导电的能力。随着转变温度接近液氧沸腾的温度，高温超导体在比传统超导体高得多的温度下仍然表现出超导性，但仍然远远低于室温。更根本的是，理论研究与实验观察相结合，有望导致对量子物质结构的更深层次的理解。该奖项支持的研究将与公开讲座、大众科学杂志上的文章、高级学生学校的讲座相结合。这项研究将由一群来自世界各地机构的学生和博士后进行。该奖项支持理论研究和教育，以调查有趣的金属材料中拓扑秩序，量子临界性和对称性破缺的相互作用。晶格模型将被开发，以适应分析研究和量子蒙特卡罗模拟。PI旨在描述有量子纠缠和没有量子纠缠的金属态之间的转变，以及拓扑顺序的作用。拓扑有序、量子临界和对称性破缺的相互作用理论在绝缘体中得到了很好的发展；PI提出了一个将这些理论扩展到金属的计划。可靠的分析和数值工具将导致对这些金属的相图的描述，以及涉及与拓扑秩序发展相关的费米表面尺寸变化的量子相变。无序对相关金属态的影响将被研究，建立在最初由PI提出的一种奇怪金属的可解Sachdev-Ye-Kitaev模型的基础上。无序在金属的电导率和热导率中起着至关重要的作用，这些电导率将在相关状态下计算。新的分析工具将被开发来分析没有准粒子激励的金属动力学。与一些实验小组的合作将使理论与铜和镍超导体以及密切相关的材料，石墨烯和其他现代材料的观察结果进行比较。

NONTECHNICAL SUMMARYThis award supports theoretical research and education to investigate unusual metallic states that arise in quantum materials and the interesting states of matter composed of electrons that emerge from these 'strange metals.' In familiar metals like copper or silver, electrical conduction occurs via the motion of a liquid of electrons through the crystal of atoms, with the quantum motion of each electron largely independent of the other electrons. However, in many modern quantum materials, and especially in the cuprate compounds which display high temperature superconductivity, the motion of an electron is correlated with that of other electrons. This correlation is of a subtle non-local quantum variety, often referred to as quantum entanglement, in which observation of one electron can determine the state of other well-separated electrons. In this project, the PI will focus on studying and classifying states of electrons with complex varieties of long-range quantum entanglement. Understanding such metallic states is required to predict the critical temperature for high temperature superconductivity, as superconductivity emerges from such a `strange' metal upon lowering the temperature. Superconductors exhibit the ability to conduct electricity without resistance when the temperature is lowered through the superconducting transition temperature. With transition temperatures near the temperature where liquid oxygen boils, high temperature superconductors still exhibit superconductivity at much higher temperatures than traditional superconductors but still very much below room temperature. More fundamentally, theoretical research in combination with experimental observations, is expected to lead to a deeper understanding of the structure of quantum matter. The research supported by this award will be coupled with public lectures, articles in popular science journals, lectures at schools for advanced students. The research will be conducted by a group of students and postdoctoral fellows drawn from institutions around the world.TECHNICAL SUMMARYThis award supports theoretical research and education to investigate the interplay of topological order, quantum criticality, and broken symmetry in interesting metallic materials. Lattice models will be developed that are amenable to analytical study and quantum Monte Carlo simulations. The PI aims to describe the transition between metallic states with and without quantum entanglement, and the role of topological order. The theory of the interplay of topological order, quantum criticality, and broken symmetry is fairly well-developed in insulators; the PI proposes a program to extend such theories to metals. Reliable analytic and numerical tools will lead to a description of the phase diagrams of such metals, and of quantum phase transitions involving changes in Fermi surface size linked to the development of topological order. The effect of disorder on correlated metallic states will be examined, building upon the solvable Sachdev-Ye-Kitaev model of a strange metal that had been originally proposed by the PI. Disorder plays a crucial role in the electrical and thermal conductivities of metals, and these conductivities will be computed in correlated states. New analytic tools will be developed to analyze the dynamics of metals without quasiparticle excitations. Collaborations with a number of experimental groups will allow comparison of theories to observations in the cuprate and pnictide superconductors and closely related materials, graphene, and other modern materials.