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，该凝聚态系统涉及许多强相互作用的电子，其行为受量子力学的强烈影响。在理解方面的进展可能会导致预测具有新性质的新物质状态以及具有潜在有用应用的新材料。强相互作用电子的一种特殊状态是“对密度波超导体”，它是液晶显示器中发现的分子的量子力学和超导类似物。它具有固体和液体的性质。PI将进一步调查这些相是否能够解释被称为高温超导体的材料的特殊性质。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。高温超导体之所以有趣，是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性。提出的物质的双密度波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是了解寻找物质新状态的实验。特别令人感兴趣的是那些被称为拓扑态的东西，它们被预测具有不寻常的性质，使基于量子力学定律的计算成为可能。这种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。研究涉及材料物理的前沿问题，并提供机会在令人兴奋的前沿培养下一代理论科学家。研究和教育将通过开发高级课程材料进一步结合起来。预测和发现电子物质新状态的进展为未来与电子设备的先进固态材料相关的技术开辟了新的可能性。技术总结该项目为凝聚态理论和相关教育的研究提供支持。我们的目标是理解包含许多强耦合自由度的凝聚态系统，这些系统的行为受量子力学的强烈影响。这种强关联体系中的电子自发地组织成电子液晶相和拓扑相。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。它们与高温超导的机制密切相关，高温超导是物理学中的一个基本问题，已经在技术上产生了强烈的影响。拓扑相是物质的量子流体状态，它没有序参量，因此不破坏任何对称性，但具有一种隐藏的量子秩序，其中基态的简并程度由它们所在空间的拓扑决定。拓扑流体的量子态是强纠缠的，这一性质可以用来设计拓扑量子计算机，这是物理和数学中的一个前沿问题，对技术具有巨大的潜在影响。将研究的相关主题包括电子液晶与高温超导的关系，量子霍尔系统中的量子相干和干涉现象，量子纠缠和拓扑量子计算。PI将使用量子场论的方法和思想，因为它们是解决涉及强相互作用系统的统计和量子物理问题的自然途径。这种方法使该项目能够利用凝聚态系统、高能物理和数学之间持续和相互丰富的思想交流。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding condensed matter systems involving many strongly interacting electrons whose behavior is governed by strong effects of quantum mechanics. Advances in 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 is the “pair-density wave superconductor”, which is a quantum mechanical and superconducting analogue of molecules found in liquid crystal displays. It shares 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 proposed pair-density wave 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 understanding experiments seeking new states of matter. Of particular interest are those 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 opportunities to train the next generation of theoretical scientists at an exciting frontier. Research and education will be further integrated through the development of advanced curricular materials. Advances from the prediction and discovery of new states of electronic matter open 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 and associated education. The objective is to understand 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. They are closely related to mechanisms of high temperature superconductivity, a fundamental problem in physics which already has had a strong impact in technology. Topological phases are quantum fluid states of matter that do not have an order parameter, and therefore do not break any symmetry, but possess a kind of hidden quantum order in which the ground state degeneracy is determined by the topology of the space in which they exist. The quantum states of a topological fluid are strongly entangled, a property that can be used to devise a topological quantum computer, a frontier problem in physics and mathematics having great potential impact on technology. Related 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 PI will use the methods and ideas of quantum field theory, because they are natural approaches to attack problems involving the statistical and quantum physics of strongly interacting systems. Such an approach enables the project to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems, high energy physics, and mathematics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.