Criticality and Order in Quantum Matter

非技术性总结该奖项支持凝聚态物理学的基础理论研究，旨在促进对物质电子态的理解，物质中的电子协同作用的结果，以组织自己表现出例如磁性和超导性的形式。 晶体中电子的集体行为受量子力学原理的支配，这些原理也决定了氢原子中单个电子的轨道。在晶体中，许多电子的量子理论意味着电子以新的方式组织自己。PI将研究这些新的秩序类型。其中最突出的是高温超导性的出现，即电子即使在液氮沸点以上的温度下也能无电阻地导电的能力。实验揭示了其他类型的秩序，其中一些在PI的早期工作中得到了预测，涉及电子密度的周期性调制。在这个项目中，PI将研究电子组织自身的多种可能方式之间的相互作用。研究将与世界各地的实验研究小组密切联系。多种有序的存在也为“量子相变”提供了可能性，在这种相变中，许多电子的量子力学状态发生集体变化。PI旨在将量子相变的性质与实验中观察到的各种性质的温度依赖性联系起来。理论研究与实验观察相结合，有望加深对量子物质结构的理解。对新物质状态的理解有助于基础知识，这些知识可以导致新技术，例如新的电子设备和低损耗电力传输。这项研究将与公开讲座、在科普期刊上发表文章、在高等学校举办讲座相结合。该研究将由来自世界各地的研究机构的一组学生和博士后研究员进行。技术总结该奖项支持竞争秩序，量子相变和超导性的基础理论研究。 对铜氧化物高温超导体的X射线散射实验揭示了一种制度，其中超导性与波动的“电荷”秩序竞争，与PI的预测一致。PI已经开发了一个更全面的模型来描述这种行为，并将在温度、电子密度和非平衡时间尺度的广泛范围内研究其后果。另一组关于磷族元素化物超导体的实验已经清楚地确定了量子相变的重要性，包括“反铁磁”秩序的开始。PI和合作者开发了新的场论和量子蒙特卡罗方法来研究量子相变，并将使用它们来理解和预测临界点附近的物理性质。这些方法和分析还将应用于双层石墨烯、超冷原子光学晶格以及与光学腔强耦合的原子系统中类似的实验相关问题。该研究将导致对具有多种可能的有序不稳定性的量子系统的相结构的更深入的了解。正在开发新的分析和数值方法来理解强耦合量子临界点，这些方法将有助于理解在许多量子材料中发现的量子临界状态。人们期望对许多种类的量子材料有一个统一的理解，并与许多实验研究密切联系。这项研究将与公开讲座、在科普期刊上发表文章以及在学校为高级学生举办讲座相结合。这项研究将由来自世界各地机构的一组学生和博士后研究员进行。

NONTECHNICAL SUMMARYThis award supports fundamental theoretical research in condensed matter physics with the aim to advance understanding of electronic states of matter, the result of electrons in materials acting in concert to organize themselves to exhibit for example forms of magnetism, and superconductivity. The collective behavior of electrons in crystals is governed by the same principles of quantum mechanics which also determine the orbits of a single electron in a hydrogen atom. In a crystal, the quantum theory of many electrons implies the appearance of novel ways electrons organize themselves. The PI will investigate these novel types of order. Prominent among these is the appearance of high temperature superconductivity, the ability of electrons to conduct electricity without resistance even at temperatures above the boiling point of liquid nitrogen. Experiments have revealed additional types of order, some of which were predicted in the PI's early work, involving periodic modulations in the density of the electrons. In this project, the PI will study the interplay between multiple possible ways electrons can organize themselves. Research will be done in close contact with experimental research groups around the world. The existence of multiple kinds of order also opens up the possibility of a "quantum phase transition" in which there is a collective change in the quantum mechanical states of many electrons. The PI aims to relate the properties of quantum phase transitions to temperature dependencies of various properties observed in experiments. The theoretical research, in combination with experimental observations, is expected to lead to a deeper understanding of the structure of quantum matter. The understanding of new states of matter contributes fundamental knowledge that can lead to new technologies, for example new electronic devices and low loss power transmission. The research 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 fundamental theoretical research on competing order, quantum phase transitions, and superconductivity. X-ray scattering experiments on the cuprate high temperature superconductors have exposed a regime where superconductivity competes with fluctuating 'charge' order, consistent with the PIs predictions. The PI has since developed a more comprehensive model of such behavior, and will investigate its consequences over wide regimes of temperatures, electron densities, and non-equilibrium time scales. Another set of experiments on the pnictide superconductors have clearly identified the importance of a quantum phase transition involving the onset of 'antiferromagnetic' order. The PI and collaborators have developed new field-theoretic and quantum Monte Carlo methods to investigate quantum phase transitions, and will use them to understand and predict physical properties near the critical point. The methods and analyses will also be applied to similar experimentally relevant issues in bilayer graphene, optical lattices of ultra-cold atoms, and to atomic systems strongly coupled to optical cavities. The research will lead to deeper insights into the phase structures of quantum systems with multiple possible ordering instabilities. New methods, analytic and numeric, are being developed to understand strongly-coupled quantum critical points, and these will help understand the regimes of quantum criticality found in numerous quantum materials. A unified understanding is expected for many classes of quantum materials, in close contact with many experimental studies. The research will be coupled with public lectures, articles in popular science journals, and 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.