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

技术总结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、整数量子霍尔效应的平台转变和量子临界现象等领域的问题。凝聚态物理中许多最有趣的或新出现的现象不能用现有的范例和技术来理解，经常需要开发新的方法或途径来描述它们。特别感兴趣的材料包括那些电子行为由强相互作用和强无序主导的材料，以及那些显示出拓扑特征的材料。由于可供研究的理论工具数量有限，对这类系统的理解往往非常具有挑战性。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的目标是在研究量子纠缠和量子信息、物质的拓扑态和拓扑绝缘体以及无序电子系统中的局域跃迁的背景下开发理论工具。计划采用的方法范围从拓扑学，到保形场理论，Schramm-Loewner演化和泛函重整化群。非技术总结该奖项支持旨在发现和研究物质的新相的理论研究和教育。后者往往表现出全新的现象，并可能具有极不寻常的特性，有望成为未来技术的基础。最近的一个例子是发现了拓扑绝缘体，这种绝缘体是整体的绝缘体，但表面是导体。另一个例子是一种名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，已被提出用来构成所谓的容错量子计算机的物理基础，它的实现将标志着一个全新计算时代的曙光。随着凝聚态物理中出现新的现象，经常需要开发新的方法或途径来描述它们。这通常发生在由强相互作用主导的电子系统中，或者由于无处不在的样品杂质而产生的强烈无序的存在。这个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。这项研究活动旨在推动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。它还将促进对研究生和博士后研究人员的培训和指导，他们与国际和平研究所就这一项目进行互动。因此，这项活动将有助于培养下一代凝聚态理论家。

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.