CAREER: Interplay of Symmetry and Topology in Condensed Matter Systems

非技术总结这个职业奖项支持物质的新量子相的理论研究和教育。相互作用的多电子系统，如那些在各种材料中发现的系统，其不同之处在于它们表现出在只由几个粒子组成的系统中不明显的紧急行为和性质。由此产生的各种物质相具有非常不同的物理性质，例如导电与绝缘、多种形式的磁性等，这些都是固态材料的重要技术应用的基础。事实证明，用来描述传统物质相的组织原理极为成功，其基础是对称性的概念。然而，最近发现了物质的奇异相，它超越了传统的智慧，并通过量子力学效应和强烈的相互作用而成为可能。例如，当电子在外部磁场中被限制在平面内时发生的分数量子霍尔效应，以及磁性材料中磁矩的类液体状态。这些新的物质相在某种意义上具有非常丰富和有序的内部结构，这就是所谓的拓扑有序。这个项目的目的是促进对拓扑有序相的理论理解。PI将研究对称性和拓扑秩序之间的相互作用如何产生新的量子现象，通过开发一个理论框架来系统地研究对称性存在时的拓扑现象，并表征由对称性丰富的物质的新的量子相。有了这些见解，PI还将探索探索实验中拓扑秩序的新方法。该项目将在凝聚态之外产生广泛影响，因为该研究触及了相关领域的基本兴趣问题，如高能物理和数学。除了研究，该项目还将寻求通过协调的外联活动来丰富当地社区的物理教育。通过与耶鲁大学科学之路计划的整合，该项目支持的外展活动将向物理学和STEM相关领域中代表性不足群体的初中生和高中生以及普通公众提供机会，旨在阐明这项研究的基础物理，并更广泛地促进对量子材料前沿研究的认识。TECHNICAL SUMMARY该职业奖项支持研究和教育，以促进对多体系统相互作用中物质的量子相的基本理解。近年来，对称性和拓扑序之间的综合为这一主题带来了新的见解，统一了量子物质研究中的几条重要线索。这项研究的重点是确定对称性在物质奇异拓扑相中的多方面作用，并表征这些系统中的普遍量子现象。PI将使用解析方法并辅之以数值模拟来解决这些问题。具体地说，本项目有以下目标：1)发展费米子系统中对称性丰富的拓扑相的理论框架。这包括对突然出现的激发和潜在的新的量子反常的对称性变换的一般分类。在此过程中，PI还将研究三维中受费米子对称性保护的内在相互作用的拓扑相，并将开发理论机制来理解对称拓扑相周围的全局相图。2)发展三维空间中带隙量子场论的物理分类，并表征环路激发的量子统计。这项研究的另一个重要方面是通过揭示其与平移对称性丰富的拓扑序的深层联系来推进对分形子拓扑相的新的理解，并潜在地应用于自旋液体材料。3)在本项目获得的理论见解的基础上，利用动力学测量来研究拓扑相的新的实验探索。PI计划探索动力学和局域测量中对称分馏的实验特征。该项目将在凝聚态社区之外产生广泛影响，因为该研究触及了相关领域的基本兴趣问题，如高能物理和数学。除了研究，该项目还将寻求通过协调的外联活动来丰富当地社区的物理教育。通过与耶鲁大学的科学之路计划相结合，该项目支持的外展活动将向物理学和STEM相关领域中代表性不足群体的初中生和高中生以及普通公众提供机会，旨在阐明这项研究背后的物理学，并更广泛地促进对量子材料前沿研究的认识。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education in novel quantum phases of matter. Interacting many-electron systems, such as those found in a great variety of materials, are distinguished in that they exhibit emergent behaviors and properties that do not manifest in systems comprised of only few particles. The resulting rich variety of phases of matter with wildly different physical properties, e.g. conducting vs. insulating, many forms of magnetism, etc., underlie important technological applications of solid-state materials. An organizing principle that has proven extremely successful for describing conventional phases of matter is based on the notion of symmetry. However, exotic phases of matter have been discovered recently that transcend conventional wisdom and which are enabled by quantum-mechanical effects and strong interactions. Examples include the fractional quantum Hall effect that occurs when electrons are confined in a plane in an external magnetic field, and liquid-like states of magnetic moments in magnetic materials. These new phases of matter have remarkably rich and ordered, in a sense, internal structure, which is termed "topological order".This project aims to advance the theoretical understanding of topologically ordered phases. The PI will investigate how the interplay between symmetry and topological order gives rise to new quantum phenomena, by developing a theoretical framework to systematically study topological phenomena in the presence of symmetries and to characterize new quantum phases of matter enriched by symmetries. With these insights the PI will also explore new ways to probe topological order in experiments.The project will achieve broad impact beyond the condensed matter community, as the research touches on problems that are of fundamental interest in related fields, such as high-energy physics and mathematics. Beyond research, the project will seek to enrich physics education in local communities with coordinated outreach activities. Through integration with the Pathways to Science program at Yale, the outreach activities supported by this project will provide opportunities to middle- and high-school students from underrepresented groups in physics and STEM-related fields, as well as to the general public, aiming to elucidate the physics underlying this research, and more broadly to promote awareness of cutting-edge research on quantum materials.TECHNICAL SUMMARYThis CAREER award supports research and education towards advancing fundamental understanding of quantum phases of matter in interacting many-body systems. In recent times, a synthesis between symmetry and topological order has brought new insights into the subject, unifying several important threads in the study of quantum matter. This research focuses on identifying the multifaceted roles of symmetries in exotic topological phases of matter and on characterizing universal quantum phenomena in these systems. The PI will use analytical methods supplemented by numerical simulations to tackle these problems. Specifically, this project has the following objectives:1) Developing a theoretical framework for symmetry-enriched topological phases in fermionic systems. This includes a general classification of symmetry transformations on emergent excitations and potentially new quantum anomalies. Along the way, the PI will also investigate intrinsically interacting fermionic symmetry-protected topological phases in three dimensions, and will develop theoretical machinery to understand global phase diagrams around symmetric topological phases.2) Developing a physical classification of gapped quantum field theories in three spatial dimensions, and characterizing quantum statistics of loop excitations. Another important aspect of this investigation is to advance new understanding of fracton topological phases by unraveling their deep connections to translation-symmetry-enriched topological order, with potential applications to spin liquid materials.3) Investigating novel experimental probes of topological phases using dynamical measurements, building on the theoretical insights gained in this project. The PI plans to explore experimental signatures of symmetry fractionalization in dynamical and local measurements.The project will achieve broad impact beyond the condensed matter community, as the research touches on problems that are of fundamental interest in related fields, such as high-energy physics and mathematics. Beyond research, the project will seek to enrich physics education in local communities with coordinated outreach activities. Through integration with the Pathways to Science program at Yale, the outreach activities supported by this project will provide opportunities to middle- and high-school students from underrepresented groups in physics and STEM-related fields, as well as to the general public, aiming to elucidate the physics underlying this research, and more broadly to promote awareness of cutting-edge research on quantum materials.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.