Quantum Field Theory for Topological Phases of Matter

物质拓扑相的量子场论

• 批准号: 2210182
• 负责人: Shu-Heng Shao
• 金额: $ 22.5万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-08-01 至 2025-07-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2210182&HistoricalAwards=false
• 关键词: Quantum; Field; Theory; Topological; Phases

This award funds the research activities of Professors Shu-Heng Shao at Stony Brook University.Symmetry has proven, time and again, to be the fundamental guiding principle in theoretical physics. Applications range from the spacetime symmetry in Einstein's theory of special relativity to the rotational symmetry in the quantum-mechanical description of the hydrogen atom and to the classification of the different phases of matter. Symmetry is one of the few universally applicable tools in analyzing quantum systems with strong interactions, and it often leads to far-reaching dynamical consequences. In recent years, the notion of symmetry has been generalized in several different directions, with interdisciplinary applications in high-energy physics, condensed-matter physics, mathematics, and quantum information theory. Professor Shao aims to develop a modern theoretical framework to discuss these new symmetries and uncover hidden symmetries in a diverse set of physical systems. Research along this line advances the national interest by reinforcing fundamental research in the United States and addressing one of the most fundamental and basic issues in the sciences, namely the role of symmetries. This project is also expected to have signiicant broader impacts. Professor Shao will mentor postdoctoral researchers through collaborations on proposed research projects. He also plans to give public lectures and organize summer schools based on his research.More technically, Professor Shao will focus on the interplay between three major kinds of generalized global symmetries: subsystem symmetries, higher-form symmetries, and non-invertible symmetries. Subsystem and higher-form symmetries are novel symmetries that do not act uniformly on the whole physical system, while non-invertible symmetries are associated with symmetry transformations that cannot be undone. Professor Shao will investigate these symmetries within the context of quantum field theory and lattice models. Within the context of subsystem symmetries, he will apply these symmetries to a new quantum phase of matter, the so-called "fracton" phase, and extend the framework of quantum field theory to describe the continuum limit of fractons. He will also study new anomalies associated with these generalized symmetries and derive nontrivial constraints on renormalization-group flows.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.

该奖项资助石溪大学邵书恒教授的研究活动。对称性已一次又一次地被证明是理论物理学的基本指导原则。 应用范围从爱因斯坦狭义相对论中的时空对称性到氢原子量子力学描述中的旋转对称性以及物质不同相的分类。 对称性是分析具有强相互作用的量子系统的少数普遍适用的工具之一，它通常会导致深远的动力学后果。 近年来，对称性的概念已在几个不同的方向得到推广，在高能物理、凝聚态物理、数学和量子信息论等领域具有跨学科应用。 邵教授的目标是开发一个现代理论框架来讨论这些新的对称性并揭示不同物理系统中隐藏的对称性。 沿着这条线的研究通过加强美国的基础研究并解决科学中最基本和最基本的问题之一（即对称性的作用）来促进国家利益。 预计该项目还将产生更广泛的重大影响。邵教授将通过拟议研究项目的合作来指导博士后研究人员。他还计划根据他的研究进行公开讲座并组织暑期学校。从技术上讲，邵教授将重点关注三种主要的广义全局对称性之间的相互作用：子系统对称性、更高形式的对称性和不可逆对称性。 子系统和更高形式的对称性是新颖的对称性，它们不会均匀地作用于整个物理系统，而不可逆对称性则与无法撤销的对称变换相关。 邵教授将在量子场论和晶格模型的背景下研究这些对称性。 在子系统对称性的背景下，他将这些对称性应用于物质的新量子相，即所谓的“分形”相，并扩展量子场论的框架来描述分形的连续极限。 他还将研究与这些广义对称性相关的新异常，并得出对重正化群流的重要约束。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。