CAREER: Interplay of Symmetry and Topology in Condensed Matter Systems

非技术性总结这个职业奖支持理论研究和教育在新的量子阶段的物质。相互作用的多电子系统，例如在各种材料中发现的系统，其区别在于它们表现出在仅由少数粒子组成的系统中不表现的涌现行为和性质。由此产生的物质相的丰富多样性，具有广泛不同的物理性质，例如导电与绝缘，多种形式的磁性等，是固态材料重要技术应用的基础。在描述物质的常规相态时，一个被证明极为成功的组织原则是基于对称性的概念。然而，最近发现了物质的奇异相，它们超越了传统的智慧，并由量子力学效应和强相互作用实现。例子包括当电子被限制在外部磁场中的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，这种结构被称为“拓扑有序”。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，通过发展一个理论框架来系统地研究对称性存在下的拓扑现象，并表征对称性丰富的物质的新量子相。有了这些见解，PI还将探索在实验中探测拓扑有序的新方法。该项目将在凝聚态领域之外产生广泛的影响，因为研究涉及相关领域的基本问题，如高能物理和数学。除研究外，该项目还将通过协调的外联活动，努力丰富当地社区的物理教育。通过与耶鲁大学的科学之路项目整合，该项目支持的外展活动将为物理和STEM相关领域代表性不足的初中和高中学生以及公众提供机会，旨在阐明这项研究背后的物理学，更广泛地提高人们对切割的认识-该职业奖支持研究和教育，以促进对量子材料的基本理解。相互作用多体系统中物质的量子相近年来，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个重要线索。这项研究的重点是确定在异国情调的拓扑相位的物质和表征这些系统中的普遍量子现象的对称性的多方面的作用。PI将使用分析方法辅以数值模拟来解决这些问题。具体而言，本项目有以下目标：1）建立费米子系统中富核拓扑相的理论框架。这包括对涌现激发和潜在的新量子异常的对称变换的一般分类。沿着，PI也将调查内在相互作用的费米子保序拓扑相在三维空间，并将开发理论机器，以了解全球相图对称拓扑相周围。2）开发一个物理分类的三维空间的有间隙的量子场论，并表征量子统计的循环激发。本研究的另一个重要方面是通过揭示分形子拓扑相与自旋对称性丰富的拓扑有序的深层联系来推进对分形子拓扑相的新理解，并具有自旋液体材料的潜在应用。PI计划在动力学和局部测量中探索对称性分馏的实验特征。该项目将在凝聚态社区之外产生广泛的影响，因为研究涉及相关领域的基本兴趣问题，例如高能物理和数学。除研究外，该项目还将通过协调的外联活动，努力丰富当地社区的物理教育。通过与耶鲁大学的科学之路项目整合，该项目支持的外展活动将为物理和STEM相关领域代表性不足的初中和高中学生以及公众提供机会，旨在阐明这项研究背后的物理学，更广泛地提高人们对切割的认识-该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准。

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.