Applications of Field Theory to Condensed Matter Physics

非技术总结该奖项支持理论研究和教育，旨在了解凝聚态系统，涉及许多强烈相互作用的电子，其行为受量子力学的强烈影响。随着认识的进步，人们可以预测具有新性质的新物质状态，以及具有潜在应用价值的新材料。强相互作用电子的一种特殊状态是“对密度波超导体”，它是液晶显示器中分子的量子力学和超导模拟物。它具有固体和液体的性质。PI将进一步研究这些相是否可以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。高温超导体是令人感兴趣的，因为它们在比许多其他已知类别的超导体高得多的温度下表现出超导性。提出的物质的对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性的材料。这可能导致电力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理解寻求新物质状态的实验。特别令人感兴趣的是那些被称为拓扑状态的状态，这些状态被预测具有不寻常的性质，可以根据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。这项研究涉及材料物理学中的前沿问题，并为在令人兴奋的前沿领域培养下一代理论科学家提供了机会。将通过编制先进的教材，进一步将研究和教育结合起来。电子物质新状态的预测和发现的进展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。技术总结本项目为凝聚态理论的研究和相关教育提供了支持。 目的是了解凝聚态系统，包括许多强耦合的自由度，其行为是由量子力学的强效应。这种强关联系统中的电子自发地组织在电子液晶相和拓扑相中。 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秩序。它们与高温超导机制密切相关，这是物理学中的一个基本问题，已经对技术产生了强烈的影响。拓扑相是物质的量子流体态，它们没有序参量，因此不会破坏任何对称性，但具有一种隐藏的量子序，其中基态简并由它们存在的空间的拓扑决定。 拓扑流体的量子态是强纠缠的，这一性质可用于设计拓扑量子计算机，这是物理学和数学中的前沿问题，对技术具有巨大的潜在影响。研究的相关课题包括电子液晶相与高温超导性之间的关系、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，因为它们是解决强相互作用系统的统计和量子物理问题的自然方法。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交叉施肥思想。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值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.