Field Theoretical Methods in Strongly Interacting and Strongly Disordered Condensed Matter Physics

该奖项支持NSF范围内数学科学优先领域的理论研究和教育。 该项目处于理论凝聚态物理和数学的交界处，凝聚态物理实验室中观察到的许多有趣现象都是由强相互作用或强无序支配的。 理解这样的系统通常是非常具有挑战性的，由于有限数量的理论工具可用于他们的描述，标准的范例，包括例如费米液体或其他独立的粒子类型的方法往往不足以捕捉在这个奖项下支持的工作的重点是应用和发展的新的理论方法，旨在处理这样的强耦合问题。 主要研究方向包括强相互作用下的量子杂质问题中的非费米液体行为、无序电子系统中的局域化跃迁以及无序和相互作用同时作用的系统。 PI将使用从共形场论到泛函重整化群以及随机Loewner演化的新兴领域的方法。非技术摘要：该奖项支持NSF范围内数学科学优先领域的理论研究和教育。 该项目位于理论凝聚态物理和数学的接口。该研究重点是凝聚态理论的前沿问题，涉及具有不寻常特性的材料或纳米系统。 这通常是电子间强相互作用的结果。 无序，即原子的位置明显偏离高度有序的排列，也可能起着重要的作用。 理解这两个因素协同作用的影响是一个巨大的理论挑战。 PI将开发新的理论工具，其中一些受益于数学科学的最新进展，以推进对材料中强相互作用和无序的综合效应的研究。 这项研究旨在推进基础科学，它本身就很有趣，也很重要. 它也可能有助于发现新的现象，并有助于我们对未来技术应用前景的复杂材料的理解。 这项研究活动将有助于下一代凝聚态理论家的教育。

TECHNICAL SUMMARY:This award supports theoretical research and education under the umbrella of the NSF-wide Mathematical Sciences Priority Area. This project lies at the interface of theoretical condensed matter physics and mathematics.Many interesting phenomena observed in the condensed matter physicslaboratory are dominated by strong interactions or strong disorder. Theunderstanding of such systems is typically very challenging, due to the limitednumber of theoretical tools available for their description, standard paradigmsincluding for example Fermi-Liquid or other independent particle-typeapproaches are often not adequate to capture theThe focus of the work supported under this award is the application and the Development of novel theoretical methods aimed at treating such strong coupling problems. The focus of the research includes Non-Fermi-Liquid behavior inQuantum Impurity Problems dominated by strong interactions, localization Transitions in disordered electronic systems, and systems dominated by thesimultaneous effects of disorder and interactions. The PI will use methodsranging from conformal field theory, to the functional renormalization group, and the emerging field of the Stochastic Loewner Evolution.NON-TECHNICAL SUMMARY:This award supports theoretical research and education under the umbrella of The NSF-wide Mathematical Sciences Priority Area. This project lies at the Interface of theoretical condensed matter physics and mathematics.This research focuses on problems at the frontiers of condensed matter theory that involve materials or nanosystems with unusual properties. These often ariseas a consequence of strong interactions among electrons. Disorder, where thepositions of the atoms deviate significantly from highly ordered arrangements,may also play an important role. Understanding the effects of these two factorsworking in concert represents a formidable theoretical challenge. The PI will,develop new theoretical tools, some that benefit from recent advances in themathematical sciences, to advance research on the combined effects of stronginteraction and disorder in materials. This research aims to advance fundamentalscience and it interesting and important in its own right. It may also contribute tothe discovery of new phenomena and contribute to our understanding of complexmaterials that hold promise for future technological applications. This research activity will contribute to the education of the next generation of condensed matter theorist.