Field Theoretical Methods in Strongly Interacting, Topological, and Disordered Condensed Matter Systems

强相互作用、拓扑和无序凝聚态物质系统中的场论方法

• 批准号: 1309667
• 负责人: Andreas Ludwig
• 金额: $ 27万
• 依托单位: University of California-Santa Barbara
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-01 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1309667&HistoricalAwards=false
• 关键词: Field; Theoretical; Methods; Strongly; Interacting

TECHNICAL SUMMARYThis award supports theoretical research and education to develop advanced theoretical tools to tackle problems in areas that include quantum entanglement, topological insulators, the plateau transition in the integer quantum Hall effect, and quantum critical phenomena. Many of the most interesting, or newly emerging phenomena in condensed matter physics cannot be understood in terms of existing paradigms and techniques, and the development of new methods or approaches for their description is often needed. Materials of particular interest include those where electronic behavior is dominated by strong interactions and strong disorder, and those exhibiting topological features. The understanding of such systems is often very challenging due to the limited number of theoretical tools available for their investigation. The focus of the work supported under this award is the development and the application of novel methods and techniques in condensed matter theory, a process that also benefits from recent advances in the mathematical sciences. The PI aims to develop theoretical tools in the context of the study of quantum entanglement and quantum information, topological states of matter and topological insulators, and localization transitions in disordered electronic systems. The methods planned to be employed range from topology, to conformal field theory, the Schramm-Loewner Evolution and the functional renormalization group. NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed at the discovery and study of novel phases of matter. The latter often exhibit completely new phenomena and may possess highly unusual properties that can hold promise to form the basis of future technologies. One recent example is the discovery of topological insulators, which are insulators in the bulk but conductors at the surface. Another example is a notion called non-Abelian statistics, a possible quantum property of electronic materials which has been proposed to form the physical underpinnings of what is known as a fault-tolerant quantum computer whose realization would mark the dawn of an entirely new era of computation. As new phenomena appear in condensed matter physics, the development of novel methods or approaches for their description is often called for. This typically occurs in electronic systems dominated by strong interactions, or by the presence of strong disorder arising from omnipresent sample impurities. The focus of this project is the development and the application of new theoretical tools in condensed matter theory, some of which benefit from recent advances in the mathematical sciences. Today's newly developed methods will belong to the standard repertoire of tools available to the next generation of researchers. This research activity aims to advance fundamental science at the frontiers of condensed matter theory, with the potential to contribute to the development of future technologies. It will also contribute to the training and mentoring of graduate students and postdoctoral researchers interacting with the PI on this project. This activity will thus contribute to the education of the next generation of condensed matter theorists.

该奖项支持理论研究和教育，以开发先进的理论工具来解决量子纠缠、拓扑绝缘体、整数量子霍尔效应中的平台跃迁和量子临界现象等领域的问题。凝聚态物理学中许多最有趣或最新出现的现象不能用现有的范式和技术来理解，通常需要开发新的方法或方法来描述它们。 特别感兴趣的材料包括电子行为由强相互作用和强无序支配的材料，以及表现出拓扑特征的材料。由于可用于其研究的理论工具数量有限，对此类系统的理解通常非常具有挑战性。该奖项支持的工作重点是凝聚态理论中新方法和技术的开发和应用，这一过程也受益于数学科学的最新进展。PI的目标是在量子纠缠和量子信息，物质和拓扑绝缘体的拓扑状态，以及无序电子系统中的局域化跃迁的研究背景下开发理论工具。计划采用的方法范围从拓扑学，共形场论，Schramm-Loewner演化和功能重整化群。非技术性总结该奖项支持旨在发现和研究物质新相的理论研究和教育。 后者往往表现出全新的现象，并可能拥有极不寻常的特性，有望成为未来技术的基础。 最近的一个例子是拓扑绝缘体的发现，拓扑绝缘体是本体绝缘体，但表面是导体。 另一个例子是一个称为非阿贝尔统计的概念，这是电子材料的一种可能的量子特性，已被提议形成所谓的容错量子计算机的物理基础，其实现将标志着一个全新时代的到来计算时代。 随着凝聚态物理学中新现象的出现，经常需要开发新的方法或方法来描述它们。 这通常发生在由强相互作用或由无所不在的样品杂质引起的强无序的存在所主导的电子系统中。该项目的重点是凝聚态理论中新理论工具的开发和应用，其中一些工具受益于数学科学的最新进展。今天新开发的方法将属于下一代研究人员可用的标准工具库。这项研究活动旨在推进凝聚态理论前沿的基础科学，并有可能为未来技术的发展做出贡献。它还将有助于培训和指导研究生和博士后研究人员与PI就该项目进行互动。因此，这项活动将有助于下一代凝聚态理论家的教育。