Applications of Field Theory to Condensed Matter Physics

技术总结该奖项支持凝聚态理论的理论研究和教育。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。PI将研究电子液晶和拓扑相。电子液晶相是强相关电子以不均匀和各向异性图案组织起来的物质状态。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。将研究的相关课题包括：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研究的问题的本质要求使用量子场论的方法和思想。这些是解决涉及强相互作用系统的统计和量子物理问题的最好工具。这种方法使PI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。该奖项支持继续培养有才华的理论科学家。在培养杰出的科学家，包括许多西班牙裔和女性科学家，以及通过开发高级课程材料将研究和教育结合起来方面，该协会有着良好的记录。非技术总结该奖项支持理论研究，目的是预测物质的新状态，并发展对其新性质的基本理解。这项研究的重点将是从相互强烈相互作用的电子中出现的物质状态，并将其限制在两个维度上。PI将进一步研究由PI及其合作者最初预测的固体中电子的状态。这些状态是与液晶显示器中发现的分子相类似的量子力学，液晶显示器具有固体和液体的属性。处于这些状态的电子以某种方式自我组织，这样它们就可以像液体一样流动，但呈现出取向和对称的图案，这让人想起原子在固体中的排列方式。PI将探讨这些状态是否能够解释高温超导体材料中不寻常的超导形式。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，使它们能够无损耗地导电，以及其他有趣的性质。高温超导体之所以令人感兴趣，是因为它们在比任何其他已知的超导体类别更高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电性的超导体。这可能导致电力的几乎无损传输和其他与能源相关的应用。这项研究的另一个重点涉及对实验的理解，寻找物质的新状态，并探索它们提出的新问题。据预测，在垂直于电子片的强磁场中，物质的新状态将存在于电子片中，这种条件可以在特殊制造的半导体材料中实现。物质的状态被称为拓扑态，据预测，这种状态具有不寻常的性质，可以根据量子力学定律进行计算。这样一台计算机可以比目前任何一台现有的计算机更快地解决某些问题。PI将部分借鉴量子信息论领域的进展和最近的实验结果，推进这些新态的理论，寻求更接近如何制造拓扑量子计算机的实现。这项研究涉及材料物理的前沿问题，为培养下一代理论科学家提供了极好的机会。研究和教育将通过开发高级课程材料进一步结合起来。它还为未来的技术打开了新的可能性。

TECHNICAL SUMMARYThis award supports theoretical research and education on the theory of condensed matter. 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. The PI will investigate electronic liquid crystal and topological phases. Electronic liquid crystal phases are states of matter in which strongly correlated electrons organize themselves in inhomogeneous and anisotropic patterns. 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 live. 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 nature of the problems that the PI studies requires the use of the methods and ideas of quantum field theory. These are the best tools with which to attack problems involving the statistical and quantum physics of strongly interacting systems. This approach enables the PI to exploit the continuing and mutually enriching cross-fertilization of ideas between condensed matter systems, high energy physics, and mathematics.This award supports the continued training of talented theoretical scientists. The PI has a strong record of training outstanding scientists, including many Hispanic and women scientists, and in integrating research and education through the development of advanced curricular materials. NONTECHNICAL SUMMARYThis award supports theoretical research with an aim to predict new states of matter and to develop fundamental understanding of their novel properties. The emphasis of the research will be on states of matter that emerge from electrons that interact strongly with each other and are confined to two dimensions. The PI will further investigate states of electrons in solids originally predicted by the PI and collaborators. These states are quantum mechanical analogs to the phases of molecules found in liquid crystal displays which share properties of both a solid and a liquid. Electrons in these states organize themselves in a way so that they can flow like a liquid but exhibit patterns of orientation and symmetry that are reminiscent of the way atoms are arranged in a solid. The PI will pursue whether these states can explain the unusual form of superconductivity in materials known as high temperature superconductors. At sufficiently low temperatures, the electrons in superconductors enter a cooperative quantum mechanical state that enables them to conduct electricity without loss, along with other interesting properties. The high temperature superconductors are interesting because they exhibit superconductivity at higher temperatures than any other known class of superconductors. The PI's proposed state of matter may help explain how this is possible and how superconductors might be discovered that exhibit superconductivity at room temperature. 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 and pursuing new questions that they raise. The new states of matter are predicted to exist in a sheet of electrons in a strong magnetic field perpendicular to the sheet, conditions that can be realized in specially fabricated semiconductor materials. The states of matter, called topological states, 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. Drawing in part from advances in the field of quantum information theory and the findings of recent experiments, the PI will advance the theory of these new states, seeking to come closer to the realization of how to make a topological quantum computer.The research engages cutting edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientist. Research and education will be further integrated through the development of advanced curricular materials. It also opens new possibilities for future technologies.