Applications of Field Theory to Condensed Matter Physics

非技术总结该奖项支持旨在理解凝聚态系统的理论研究和教育，凝聚态系统的行为受量子力学的强烈效应和其组成电子之间的强烈相互作用的支配。这样的理解可能导致对具有新性质的物质的新状态的预测，以及发现具有潜在有用应用的新材料。PI和他的合作者预测了物质中存在强相互作用的量子态，称为相互缠绕的有序，其中电子以复杂的模式自我组织。交织有序描述的是由于组成电子之间的强烈相互作用，不同和看似相互竞争的组织类型共存并以几乎相等的强度一起出现的物理系统。超导体就是一个相关的例子。在这些材料中，在足够低的温度下，电子进入合作量子力学状态，使它们能够在没有任何电阻的情况下导电。高温超导体是一个特别有趣的物种，因为它们在比许多其他已知的超导体类别更高的温度下表现出超导电性。PI提出的物质状态可能有助于解释这是如何可能的，以及如何发现在室温下表现出超导电性的材料。这可能导致电力和其他与能源相关的应用几乎无损传输。这项研究的另一个重点涉及对物质新状态的理解，这种状态被称为拓扑相，基本上不会受到无序和其他缺陷对材料性质造成的通常是破坏性的影响。据预测，拓扑相具有不同寻常的性质，可以根据量子力学定律进行计算。量子计算机可以比目前任何现有的计算机更快地解决某些问题。这项研究涉及材料物理中的前沿问题，并为培养下一代理论科学家提供了绝佳的机会。它还为与用于电子设备的先进固态材料相关的未来技术开辟了新的可能性。研究和教育将通过高级课程材料的开发进一步整合。技术总结该奖项支持旨在了解凝聚态系统的理论研究和教育，这些凝聚态系统涉及许多强耦合自由度，其行为受到量子力学的强烈影响。这种强关联体系中的电子自发地在电子液晶相和拓扑相中组织。这些阶段的一个不可避免的特点是，它们自然地描述了相互交织的顺序。该项目的主要关注点是强关联系统中相互交织的有序理论，以及物质的拓扑相。这两条研究路线都需要发展新的理论见解，并使用量子场论的方法和思想。这些项目包括在微观模型中研究双密度波超导态的出现，包括在准一维环境和梯形系统中，发展双密度波和电荷4E超导态的有效场论，以及揭示电子向列相有序和超导电性之间的联系机制。PI关于物质拓扑相的工作旨在建立电子向列相有序和成对量子霍尔态(一种相互缠绕的有序形式)之间的关系，并致力于发展受挫量子反铁磁体的晶格Chern-Simons规范理论，并将其应用于分馏Chern绝缘体理论。一个重要的新项目旨在找出早期PI发展的量子临界回路理论与最近猜测的狄拉克系统的量子对偶之间的关系。这项研究涉及材料物理的前沿问题，并为培养下一代理论科学家提供了极好的机会。它还为与用于电子设备的先进固态材料相关的未来技术开辟了新的可能性。研究和教育将通过开发高级课程材料进一步结合起来。

NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding condensed matter systems whose behavior is governed by strong effects of quantum mechanics and strong interactions between their constituent electrons. Such understanding could lead to the prediction of new states of matter with novel properties as well as to the discovery of new materials with potentially useful applications. The PI and his collaborators have predicted the existence of strongly interacting quantum states of matter, named intertwined orders, in which electrons organize themselves in complex patterns. Intertwined orders describe physical systems in which, due to the strong interactions between the constituent electrons, different and seemingly competing types of organization coexist and emerge together with nearly equal strength. Superconductors are a relevant example. These are materials in which, at sufficiently low temperatures, electrons enter a cooperative quantum mechanical state that enables them to conduct electricity without any resistance. High-temperature superconductors are a particularly interesting species because they exhibit superconductivity at much higher temperatures than many other known classes of superconductors. The PI's proposed state of matter may help explain how this is possible, and how materials that exhibit superconductivity at room temperature might be discovered. This could lead to virtually lossless transmission of electric power and other energy-related applications. The other focus of the research concerns the understanding of new states of matter, called topological phases, which are essentially immune to the usually destructive effects that disorder and other defects have on material properties. Topological phases are predicted to have unusual properties that could enable computation based on the laws of quantum mechanics. A quantum computer could solve certain problems much faster than any currently existing computer.  The research involves cutting-edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices. Research and education will be further integrated through the development of advanced curricular materials.TECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding condensed matter systems involving many strongly coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics. The electrons in such strongly correlated systems organize spontaneously in electronic liquid-crystal phases and in topological phases. An unavoidable feature of these phases is that they naturally describe intertwined orders. The main focus of the project is on the theory of intertwined orders in strongly correlated systems, and on topological phases of matter. Both lines of research require the development of new theoretical insights and the use of methods and ideas from quantum field theory. The projects include studies of the emergence of pair-density-wave superconducting states in microscopic models, both in a quasi-one-dimensional setting and in ladder systems, developing an effective field theory of pair-density-wave and charge 4e superconducting states, and uncovering the mechanism connecting electronic nematic order and superconductivity. The PI's work on topological phases of matter aims to establish a relation between electronic nematic order and paired quantum Hall states (a form of intertwined orders), and to develop the lattice Chern-Simons gauge theory of frustrated quantum antiferromagnets, with applications to the theory of fractionalized Chern insulators. An important new project aims at finding a relation between the theory of quantum critical loops that the PI developed earlier and the recently conjectured quantum dualities for Dirac systems.The research involves cutting-edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices. Research and education will be further integrated through the development of advanced curricular materials.