Entanglement Physics of Quantum f-electron Materials

该奖项支持凝聚态物理的理论研究和教育，在f电子物理和量子物质的子领域。物质在原子尺度上的行为是由量子力学控制的，量子力学将粒子的运动描述为一种波，根据薛定谔波动方程进化。虽然这个方程在孤立电子上的应用已经被完全理解，但是这个方程的相应的多体版本（控制物质内部电子的集体量子行为）太复杂了，无法详细解决。只要注意到一磅铁中的电子数量比已知宇宙中的恒星数量还要多，就可以把握这种复杂性的天文尺度。量子力学的奇怪表现之一是一种被称为纠缠的现象，即物质中的远程电子与其运动密切相关。由这种纠缠产生的电子的意想不到的集体行为有能力赋予量子物质一些涌现的特性，比如磁性、超导性或超流动性，以及更多可能尚未被发现的特性。探索理解和操纵这些涌现的特性，并将它们与潜在的量子力学联系起来，是现代凝聚态物理学的一个关键目标。该奖项支持f电子材料领域的研究，f电子材料是一类独特的金属，可以被微调到磁性的边缘，在那里它们发展出一种特殊的量子态，称为“量子临界点”。量子临界点可以被认为是一种电子干细胞——一种物质状态，它可以很容易地将自己转化为一大类新的量子相，比如非常规的超导体。通过对这些量子临界点和它们可以转化为的相进行新的数学描述，PI旨在获得对量子材料物理学的新理解。研究生和博士后将以重要的方式参与研究，并将在广泛的理论技术方面得到指导和培训。PI还计划写一本畅销书，向非专家介绍量子凝聚态物理的前沿。该奖项支持凝聚态物理的理论研究和教育，在f电子物理的子领域。这项研究有三个主要的小标题：1)量子临界性的新方法：使用一种新的Schwinger玻色子方法，并与实验学家合作，研究小组将开发一种重电子材料的铁磁量子临界性理论。这项工作将扩展到反铁磁体，并将用于计算重费米子的广义相图。研究小组将开发一种磁性和近藤效应共存的理论。通过扩展Larkin和Pikin的早期工作，该研究将发展一种有限温度一阶相变到绝对零度量子临界点的量子退火理论。2)稀土材料中纠缠和新秩序的分析计算方法：与纽约Flatiron研究所的理论家合作，研究小组将把矩阵乘积态方法应用于简单的一维和二维近藤晶格，重点关注近藤绝缘体的低纠缠情况，使用这些方法建立和探索重费米子的复合性质。3)拉曼和光发射现象学的新方法：将光学晶格理论推广到晶体场，研究将发展f电子材料中光与晶体场能级的拉曼相互作用理论。提出了一种用角分辨和核能级x射线光发射测量f电子局域化程度的新判据。研究生和博士后将以重要的方式参与研究，并将在广泛的理论技术方面得到指导和培训。PI还计划写一本畅销书，向非专家介绍量子凝聚态物理的前沿。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical research and education in condensed matter physics, in the subfield of f-electron physics and quantum matter.The behavior of matter on atomic scales is governed by quantum mechanics, which describes the motion of particles as a wave, evolving according to the Schrodinger wave equation. While the application of this equation to isolated electrons is fully understood, the corresponding many-body version of this equation that governs the collective quantum behavior of electrons inside matter is far too complex to be solved in detail. The astronomical scale of this complexity may be grasped by noting that the number of electrons in a pound of iron is larger than the number of stars in the known universe.One of the strange manifestations of quantum mechanics is a phenomenon known as entanglement, whereby remote electrons in a material intimately correlate their motion. The unexpected collective behavior of electrons that results from this entanglement has the capacity to endow quantum matter with emergent properties, such as magnetism, superconductivity, or superfluidity, and many more that are presumably not yet discovered. The quest to understand and manipulate these emergent properties, and to relate them to the underlying quantum mechanics is a key goal of modern condensed matter physics.The award supports research in the area of f-electron materials, a unique class of metals that can be fine-tuned to the brink of magnetism where they develop a special quantum state called a "Quantum Critical Point". Quantum critical points can be thought of as a kind of electronic stem cell - a state of matter that can easily transform itself into a broad class of novel quantum phases, such as unconventional superconductors. By developing a new mathematical description of these quantum critical points and the phases they can transform into, the PI aims to gain a new understanding of the physics of quantum materials.Graduate students and postdocs will be involved in an essential way in the research, and will be mentored and trained in a broad range of theoretical techniques. The PI also plans to write a popular book introducing the frontier of quantum condensed matter physics to non-experts. TECHNICAL SUMMARYThis award supports theoretical research and education in condensed matter physics, in the subfield of f-electron physics. The research has three main subheadings: 1) New approach to quantum criticality: Using a new Schwinger boson method, and working in conjunction with experimentalists, the research team will develop a theory of ferromagnetic quantum criticality in heavy-electron materials. This work will be extended to antiferromagnets and will be used to compute the generalized phase diagram of heavy fermions. The research team will develop a theory for the co-existence of magnetism and the Kondo effect. By extending early work of Larkin and Pikin, the research will develop a theory for the quantum annealing of finite-temperature first-order phase transitions into quantum critical points at absolute zero. 2) Analytic-computational approach to entanglement & novel order in rare-earth materials: Working with theorists at the Flatiron Institute, New York, the research team will apply Matrix Product State approaches to simple one- and two-dimensional Kondo lattices, focusing on the low-entanglement case of the Kondo insulator, using these methods to establish and explore the composite nature of heavy fermions.3) A new approach to Raman and Photoemission phenomenology: Generalizing the theory of optical lattices to crystal fields, the research will develop a theory of the Raman interaction of light with crystal-field levels in f-electron materials. A new criterion for measuring the degree of localization of f-electrons using angle-resolved and core-level x-ray photoemission will be developed.Graduate students and postdocs will be involved in an essential way in the research, and will be mentored and trained in a broad range of theoretical techniques. The PI also plans to write a popular book introducing the frontier of quantum condensed matter physics to non-experts.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.