Criticality and Order in Quantum Matter

该奖项支持凝聚态物理的基础理论研究，旨在促进对物质电子状态的理解，即材料中电子协同作用的结果，以组织自己表现出例如磁性和超导形式。晶体中电子的集体行为受到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，多电子的量子理论暗示了电子自我组织的新方式的出现。PI将调查这些新型的秩序。其中最突出的是高温超导性的出现，即电子在液氮沸点以上的温度下无电阻导电的能力。实验揭示了其他类型的有序，其中一些是在PI的早期工作中预测到的，涉及电子密度的周期性调制。在这个项目中，PI将研究电子自我组织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。多种有序的存在也开启了“量子相变”的可能性，在这种情况下，许多电子的量子力学状态会发生集体变化。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，有望使人们对量子物质的结构有更深入的了解。对物质新状态的理解有助于产生新技术的基础知识，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、在大众科学杂志上发表文章、在高级学生学校讲课相结合。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。该奖项支持竞争秩序、量子相变和超导的基础理论研究。铜高温超导体的x射线散射实验揭示了超导性与波动“电荷”顺序竞争的机制，与pi的预测一致。此后，PI开发了一个更全面的这种行为模型，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。另一组关于镍基超导体的实验已经清楚地确定了涉及“反铁磁”序开始的量子相变的重要性。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类似的实验相关问题，如双层石墨烯，超冷原子的光学晶格，以及与光学腔强耦合的原子系统。这项研究将导致更深入地了解具有多种可能的有序不稳定性的量子系统的相结构。新的方法，分析和数值，正在开发，以理解强耦合量子临界点，这些将有助于理解在许多量子材料中发现的量子临界状态。期望对许多种类的量子材料有一个统一的认识，并与许多实验研究密切联系。该研究将与公开演讲、在大众科学杂志上发表文章、在高级学生学校进行讲座相结合。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。

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.