CAREER: Interplay of Symmetry and Topology in Condensed Matter Systems

职业：凝聚态系统中对称性和拓扑的相互作用

• 批准号: 1846109
• 负责人: Meng Cheng
• 金额: $ 50万
• 依托单位: Yale University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2019
• 资助国家: 美国
• 起止时间: 2019-04-01 至 2024-03-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1846109&HistoricalAwards=false
• 关键词: CAREER; Interplay; Symmetry; Topology; Condensed

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.

非技术摘要这一职业奖支持物质新型量子阶段的理论研究和教育。相互作用的多电子系统（例如在各种材料中发现的系统）的区别是因为它们表现出了仅在仅由少数粒子组成的系统中表现出的新兴行为和特性。物质的各个阶段都具有截然不同的物理特性，例如进行与绝缘，多种形式的磁性等，是固态材料的重要技术应用。事实证明，在描述物质的传统阶段非常成功的组织原理是基于对称性的概念。但是，最近发现了物质的外来阶段，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来实现。示例包括当电子限制在外部磁场中的平面中以及磁性材料中磁矩的液态状态时发生的分数量子厅效应。从某种意义上说，这些新的物质阶段非常丰富和有序，被称为“拓扑顺序”。本项目旨在提高对拓扑秩序阶段的理论理解。 PI将通过开发一个理论框架来在存在对称性的情况下系统地研究拓扑现象并表征对符号富含物质的新量子阶段，从而研究对称和拓扑顺序之间的相互作用如何产生新的量子现象。有了这些见解，PI还将探索实验中探测拓扑顺序的新方法。该项目将在凝聚态物质社区以外产生广泛的影响，因为研究涉及对相关领域的基本兴趣的问题，例如高能物理学和数学。除了研究之外，该项目还将寻求通过协调的外展活动在当地社区中丰富物理教育。通过与耶鲁大学的科学课程途径的整合，该项目支持的外展活动将为来自代表性不足的物理和STEM相关领域中代表性不足的群体的高中生提供机会相互作用多体系统中物质的量子阶段。近来，对称和拓扑顺序之间的综合已为该主题带来了新的见解，从而统一了量子问题研究中的几个重要线索。这项研究重点是确定对称性在物质的外来拓扑阶段的多面作用，并在这些系统中表征普遍的量子现象。 PI将使用补充数值模拟的分析方法来解决这些问题。具体而言，该项目具有以下目标：1）在费米金系统中为对称性增强的拓扑阶段开发一个理论框架。这包括对紧急激发和潜在的新量子异常的对称转换的一般分类。一路走来，PI还将研究三个维度的内在相互作用的费米对称性拓扑阶段，并将开发理论机制，以了解对称拓扑阶段围绕对称拓扑阶段的全局相图。这项研究的另一个重要方面是通过揭示其与翻译对称性的拓扑顺序的深入联系，以提高对法acton拓扑阶段的新理解，并潜在地适用于旋转液体材料。3）研究使用动力学测量的新型实验探针，建立在该项目中的理论洞察力上。 PI计划探索动态和局部测量中对称性分数的实验性特征。该项目将在凝聚态物质社区以外产生广泛的影响，因为研究涉及对相关领域的基本兴趣的问题，例如高能量物理学和数学。除了研究之外，该项目还将寻求通过协调的外展活动在当地社区中丰富物理教育。通过与耶鲁大学的科学课程融合的整合，该项目支持的外展活动将为来自代表性不足的物理和与STEM相关领域的群体不足的中学和高中生提供机会，以及向公众提供的机会，旨在阐明这项研究的基础物理学，并更广泛地促进对量化材料的宣传和统计范围的宣传。通过基金会的智力优点和更广泛的影响评估标准通过评估来支持。

项目成果

Relative anomaly in ( 1+1 )d rational conformal field theory

• DOI: 10.1103/physrevresearch.2.043044
• 发表时间: 2020-02
• 期刊: arXiv: Strongly Correlated Electrons
• 作者: M. Cheng;D. Williamson

Designer non-Abelian fractons from topological layers

从拓扑层设计非阿贝尔分形

• DOI: 10.1103/physrevb.107.035103
• 发表时间: 2023
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Williamson, Dominic J.;Cheng, Meng
• 通讯作者: Cheng, Meng

Higher-form symmetry breaking at Ising transitions

• DOI: 10.1103/physrevresearch.3.033024
• 发表时间: 2020-11
• 期刊: Physical Review Research
• 影响因子: 4.2
• 作者: Jiarui Zhao;Zheng Yan;M. Cheng;Z. Meng

Generalized Lieb-Schultz-Mattis theorem on bosonic symmetry protected topological phases

玻色子对称性保护拓扑相的广义利布-舒尔茨-马蒂斯定理

• DOI: 10.21468/scipostphys.11.2.024
• 发表时间: 2019-03
• 期刊: SciPost Physics
• 影响因子: 5.5
• 作者: Jiang Shenghan;Cheng Meng;Qi Yang;Lu Yuan-Ming
• 通讯作者: Lu Yuan-Ming

Sorting topological stabilizer models in three dimensions

三维拓扑稳定器模型排序

• DOI: 10.1103/physrevb.100.155137
• 发表时间: 2019
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Dua, Arpit;Kim, Isaac H.;Cheng, Meng;Williamson, Dominic J.
• 通讯作者: Williamson, Dominic J.