Applications of Field Theory to Condensed Matter Physics

场论在凝聚态物理中的应用

• 批准号: 1064319
• 负责人: Eduardo Fradkin
• 金额: $ 45万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2011
• 资助国家: 美国
• 起止时间: 2011-09-15 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1064319&HistoricalAwards=false
• 关键词: Applications; Field; Theory; Condensed; Matter

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.

该奖项支持凝聚态理论的理论研究和教育。目标是了解涉及许多强耦合自由度的凝聚态物质系统，其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。PI将研究电子液晶和拓扑相。电子液晶相是物质的一种状态，在这种状态下，强相关电子以非均匀和各向异性的模式组织起来。拓扑相是物质的量子流体状态，没有秩序参数，因此不会破坏任何对称性，但具有一种隐藏的量子秩序，其中基态简并取决于它们所处空间的拓扑结构。拓扑流体的量子态是强纠缠态，这一特性可用于设计拓扑量子计算机，是物理和数学领域的前沿问题，对技术具有巨大的潜在影响。相关研究课题包括：电子液晶相与高温超导的关系、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研究的问题的性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佳工具。这种方法使PI能够利用凝聚态系统、高能物理和数学之间的持续和相互丰富的思想交流。这个奖项支持继续培养有才华的理论科学家。PI在培养杰出的科学家，包括许多西班牙裔和女性科学家，以及通过开发先进的课程材料将研究与教育结合起来方面有着良好的记录。该奖项支持理论研究，旨在预测物质的新状态，并发展对其新特性的基本理解。这项研究的重点将放在由电子产生的物质状态上，这些电子相互作用强烈，并且被限制在二维空间内。PI将进一步研究PI和合作者最初预测的固体中的电子状态。这些状态在量子力学上类似于在液晶显示器中发现的分子相，它们同时具有固体和液体的特性。这些状态下的电子以某种方式组织自己，使它们能够像液体一样流动，但表现出方向和对称的模式，这让人想起原子在固体中的排列方式。PI将研究这些状态是否可以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，使它们能够不损失地导电，并具有其他有趣的特性。高温超导体很有趣，因为它们在比任何其他已知超导体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，以及如何发现超导体在室温下表现出超导性。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实验的理解，寻求物质的新状态，并追求他们提出的新问题。新的物质状态被预测存在于垂直于电子片的强磁场中的电子片中，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。从量子信息理论领域的进步和最近实验的发现中，PI将推进这些新状态的理论，寻求更接近于实现如何制造拓扑量子计算机。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。它还为未来的技术开辟了新的可能性。