Applications of Field Theory to Condensed Matter Physics

该奖项支持旨在理解涉及许多耦合自由度的凝聚态系统的理论研究，这些系统的行为受量子力学的强效应控制，特别是电子之间的强相互作用。这样的理解可能会导致具有新特性的物质的新状态的预测，以及具有潜在有用应用的新材料。PI和他的合作者最初预测的一种强相互作用电子的特殊状态出现在所谓的电子液晶相中，这是液晶显示器中发现的分子的量子力学模拟，具有固体和液体的双重特性。PI将进一步研究这些相是否可以解释高温超导体材料的特殊性质。在足够低的温度下，超导体中的电子进入一种合作的量子力学状态，使它们能够在没有任何电阻的情况下导电。高温超导体很有趣，因为它们在比许多其他已知超导体高得多的温度下表现出超导性。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性的材料。这可能会导致电能和其他能源相关应用的几乎无损传输。研究的另一个重点是对寻找物质新状态的实验的理解，特别是所谓的拓扑状态，这种状态被预测具有不寻常的特性，可以基于量子力学定律进行计算。这样的计算机可以比任何现有的计算机更快地解决某些问题。该研究涉及材料物理学的前沿问题，并为培养下一代理论科学家提供了极好的机会。通过开发先进的教材，研究和教育将进一步结合起来。它还为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。技术概述：本项目为涉及许多强耦合自由度的凝聚态系统的理论研究提供支持，这些系统的行为受量子力学的强效应支配。这种强相关系统中的电子在电子液晶相和拓扑相中自发组织。这些阶段的一个不可避免的特征是，它们自然地描述了相互交织的顺序。主要项目集中在强相关系统和物质的拓扑相的交织秩序的理论。这两条研究路线都需要发展新的和变革性的理论见解，并使用量子场论的方法和思想。将研究的特定主题包括电子液晶相与高温超导之间的关系，量子霍尔系统中的量子相干性和干涉现象，量子纠缠和拓扑量子计算。该研究涉及材料物理学的前沿问题，并为培养下一代理论科学家提供了极好的机会。通过开发先进的教材，研究和教育将进一步结合起来。它还为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。

NON-TECHNICAL SUMMARYThis award supports theoretical research aimed at understanding condensed matter systems involving many coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics, in particular strong interactions between electrons. Such understanding could lead to the prediction of new states of matter with novel properties as well as new materials with potentially useful applications. A particular state of strongly interacting electrons originally predicted by the PI and his collaborators emerges in the so-called electronic liquid crystal phase, which is a quantum mechanical analogue of molecules found in liquid crystal displays, sharing properties of both a solid and a liquid. The PI will further investigate whether such phases can explain the peculiar properties of materials known as high temperature superconductors. At sufficiently low temperatures, electrons in superconductors enter a cooperative quantum mechanical state that enables them to conduct electricity without any resistance. High temperature superconductors are interesting 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 temperatures 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 experiments seeking new states of matter, in particular the so-called topological states, which are predicted to have unusual properties that would enable computation based on the laws of quantum mechanics. Such a computer could solve certain problems much faster than any currently existing computer. The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. Research and education will be further integrated through the development of advanced curricular materials. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices.TECHNICAL SUMMARYThis project provides support for research into the theory of 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 topological phases. An unavoidable feature of these phases is that they naturally describe intertwined orders. The main projects focus 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 and transformative theoretical insights and the use of methods and ideas of quantum field theory. The particular topics that will be investigated include the relation between electronic liquid crystal phases and high temperature superconductivity, quantum coherence and interference phenomena in quantum Hall systems, quantum entanglement and topological quantum computing.The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. Research and education will be further integrated through the development of advanced curricular materials. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices.