Non-Perturbative Approaches to Condensed-Matter Physics

材料研究部和数学科学部为NSF范围内的数学科学优先领域下的该奖项提供资金。该奖项支持凝聚态物理学的基础理论研究和教育，旨在发现和理解由于电子之间的强相关性而产生的物质的新有序状态。 这项研究位于理论物理和数学的界面，通常涉及并行协同推进理论凝聚物理和数学。PI将寻找物质的新相。目标包括：发现和描述具有拓扑顺序的相，其中准粒子激发不具有电子的量子数，而是它们被“分数化”;导出具有非阿贝尔编织的粒子的精确结果，其中物理学不仅取决于哪些粒子被互换，而且取决于它们互换的顺序;发现并描述将新相与常规有序相分离的量子临界点;深入探索强关联电子的一维和二维模型的对称结构，特别是不同竞争顺序之间的相互作用;在量子杂质问题中使用可积场论来描述，例如，观察到的由极稀磁性杂质对相干性的破坏。使用的一种方法将是场论，特别是用于理解传统方法无法接近的新相位的非微扰方法。其他的方法还包括可积性和超对称性，它们是在强关联系统中使精确计算成为可能的对称性。该奖项支持理论凝聚态物理和数学之间的本科生、研究生和博士后教育。非技术性概述：材料研究部和数学科学部为该奖项提供资金，该奖项属于NSF范围内的数学科学优先领域。该奖项支持凝聚态物理学的基础理论研究和教育，旨在发现和理解物质的新状态和它们之间的转换。这项研究位于理论物理和数学的界面，通常涉及并行协同推进理论凝聚物理和数学。PI专注于强磁场中被限制在二维空间的电子。已知的奇异物质状态是已知存在的;该地区已经成熟，可以发现更多的新相。有大量的证据表明，奇异相也发生在材料中，其中原子尺度磁体的排列在人类尺度上产生磁性是“受挫”的，这通常是因为原子尺度磁体在纳米尺度上的几何构型。寻找这些新的物质相的一个动机是找到一个能够成为拓扑量子计算机的系统。这样的计算机可以比任何现有的计算机更快地执行某些操作。其他不可预见的技术也可能出现。另一个动机是对物理世界的基本理解，无论它是否会导致新技术，甚至还没有想象出来。这一探索导致了理论凝聚态物理学和数学的协同进步。

TECHNICAL SUMMARY:The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at discovering and understanding new ordered states of matter that arise as a consequence of strong correlations among electrons. This research lies at the interface of theoretical physics and mathematics and often involves synergistically advancing theoretical condensed physics and mathematics in parallel. The PI will search for new phases of matter. Objectives include: finding and describing phases with topological order, where quasiparticle excitations do not have the quantum numbers of the electron, rather they are "fractionalized;" deriving exact results for particles with non-abelian braiding, where the physics depends on not only which particles are interchanged, but also the order in which they are interchanged; discovering and describing quantum critical points which separate novel phases from phases with conventional order; probing deeply the symmetry structure of one- and two-dimensional models of strongly correlated electrons, in particular the interplay between different competing orders; using integrable field theory in quantum impurity problems, to describe, for example, the observed destruction of coherence by extremely dilute magnetic impurities.One method utilized will be field theory, especially non-perturbative methods useful for understanding novel phases which cannot be approached by conventional methods. Other methods used include integrability and supersymmetry, which are symmetries making exact computations possible in strongly-correlated systems.This award supports undergraduate, graduate, and post doctoral education at the interface of theoretical condensed matter physics and mathematics.NON-TECHNICAL SUMMARY:The Division of Materials Research and the Division of Mathematical Sciences contribute funding to this award under the NSF-wide Mathematical Sciences Priority Area. This award supports fundamental theoretical research and education in condensed matter physics aimed at discovering and understanding new states of matter and transformations among them. This research lies at the interface of theoretical physics and mathematics and often involves synergistically advancing theoretical condensed physics and mathematics in parallel. The PI focuses on electrons confined to two-dimensions in a strong magnetic field. Exotic states of matter known are known to exist; the area is ripe for the discovery of more new phases. There is substantial evidence that exotic phases also occur in materials in which the alignment of atomic-scale magnets to produce magnetism on the human scale is "frustrated" often because of the geometric configuration of the atomic-scale magnets on the nanometer scale. One motivation to seek these new phases of matter is to find a system capable of becoming a topological quantum computer. Such a computer could perform certain operations much faster than any currently existing computer. Other unforeseen technologies may also arise. Another motivation is a fundamental understanding of the physical world around whether or not it leads to new technologies, not yet even imagined. The quest leads to the synergistic advance of theoretical condensed matter physics and mathematics.