Criticality and Order in Quantum Matter

非技术总结该奖项支持凝聚态物理学的基础理论研究，目的是促进对物质的电子状态的理解，物质中的电子协同作用的结果，以展示例如磁性和超导的形式。晶体中电子的集体行为受到同样的量子力学原理的支配，量子力学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起来。私家侦探将调查这些新颖的秩序类型。其中最突出的是高温超导的出现，即即使在高于液氮沸点的温度下，电子也能够在没有电阻的情况下导电。实验揭示了其他类型的有序，其中一些是在PI的早期工作中预测的，涉及电子密度的周期性调制。在这个项目中，PI将研究多种可能的电子自我组织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进行。多种有序的存在也开启了一种“量子相变”的可能性，在这种相变中，许多电子的量子力学状态发生集体变化。PI的目的是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。理论研究与实验观测相结合，有望加深对量子物质结构的理解。对新物质状态的了解有助于基础知识的发展，这些基础知识可以带来新的技术，例如新的电子设备和低损耗的电力传输。这项研究将与公开讲座、科普期刊上的文章、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研究员进行。技术总结该奖项支持关于竞争秩序、量子相变和超导的基础理论研究。在铜酸盐高温超导体上的X射线散射实验揭示了超导电性与起伏的‘电荷’顺序竞争的区域，这与PI预测一致。自那以后，PI已经开发了一个更全面的这种行为的模型，并将在温度、电子密度和非平衡时间尺度的广泛区域内调查其后果。另一组关于pNictide超导体的实验已经清楚地确认了量子相变的重要性，该相变涉及到反铁磁序的开始。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。这些方法和分析也将应用于双层石墨烯、超冷原子的光学晶格以及强耦合到光腔的原子系统中类似的实验相关问题。这项研究将使人们对具有多种可能的有序不稳定性的量子系统的相结构有更深入的了解。为了理解强耦合的量子临界点，人们正在开发新的解析和数值方法，这些方法将有助于理解在众多量子材料中发现的量子临界状态。在与许多实验研究密切联系的情况下，预计将对许多类别的量子材料有统一的认识。这项研究将与公开讲座、科普期刊上的文章以及高级学生学校的讲座结合在一起。这项研究将由一群来自世界各地机构的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.