Strong Interactions, Topology, and Constraints in Emerging Phases of Matter

该奖项支持研究和教育，以了解三维物质新相的特性，以及低维量子系统的动力学。现代物理学的前沿之一是了解在具有许多相互作用的粒子的系统中可能发生的新型量子现象。20世纪发现的这种现象的显著例子包括超流动性、超导性和分数量子霍尔效应，所有这些都需要宏观数量的相互作用粒子进入相干量子态。最近，我们对量子多粒子系统的具体抽象性质（技术术语，拓扑性质）如何影响其实际物理性质的理解取得了快速进展，导致了新材料类别的发现，如拓扑绝缘体和超导体。尤其是后者，作为量子计算的潜在平台引起了人们的兴趣，在量子计算中，信息可以以一种本质上对随机噪声具有鲁棒性的方式存储。这项研究集中在两个主题上，这两个主题既可以扩展我们对新型可能的量子现象的理解，也可以研究强相互作用如何潜在地帮助确定有前途的量子计算平台。第一个主题是扩展我们对拓扑性质如何在三维中导致新型相互作用量子物质的理解。第二个主题是理解强相互作用，以及最终在这些系统中已经被充分理解的各种拓扑性质，如何帮助塑造量子系统在有限温度下的时间演化。该项目将通过培训研究生，以及通过PI协调的项目和活动，促进明尼苏达大学感兴趣的物理学本科生和研究生向私营部门工作的过渡，为训练有素的STEM专业人员提供劳动力。这包括与工程部门合作，让感兴趣的物理本科生参与高级工程设计项目，以及帮助协调专门针对物理学生的课外网络和职业信息活动。该奖项支持研究和教育，以理解拓扑和约束在两个领域的作用：三维物质的新阶段和低维系统的动力学。在三维物质相领域，建议的研究将集中在最近发现的物质分相上，这些分相具有不寻常的特征，即它们的低洼激发限制了迁移率。在物质的相互作用的对称保护相的研究中发展起来的分析群上同的场理论技术和工具的组合将用于解决以下问题。首先，哪些场论表现出分数相的定性特征？其次，这些系统和相关系统中的对称性何时导致受保护的无间隙边界模式？解决这些问题将扩展我们对这些系统中几何和拓扑之间的相互作用如何导致与其他三维量子相不同的物理性质的理解。在低维系统动力学领域，重点将是探索约束和拓扑顺序对动力学的影响。提出的研究将使用数值（精确对角化）和基于微扰理论和随机矩阵理论的分析方法相结合。随着接近约束系统的低维系统在实验上变得可访问，阐明约束是否、何时以及如何导致量子多体系统中异常缓慢的动力学，可以显着推进我们对信息如何在量子多体系统中在中间时间尺度上更健壮地存储的理解。该项目将通过培训研究生，以及通过PI协调的项目和活动，促进明尼苏达大学感兴趣的物理学本科生和研究生向私营部门工作的过渡，为训练有素的STEM专业人员提供劳动力。这包括与工程部门合作，让感兴趣的物理本科生参与高级工程设计项目，以及帮助协调专门针对物理学生的课外网络和职业信息活动。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports research and education towards understanding the properties of new phases of matter in three dimensions, and the dynamics of low-dimensional quantum systems. One of the frontiers of modern physics is understanding what new types of quantum phenomena can occur in systems with many interacting particles. Striking examples of such phenomena discovered in the 20th century include superfluidity, superconductivity, and the fractional quantum Hall effect, all of which entail macroscopic numbers of interacting particles entering a coherent quantum state. More recently, rapid progress in our understanding of how specific abstract properties (in technical terms, topological properties) of quantum many-particle systems influence their real physical properties has led to the discovery of new classes of materials, such as topological insulators and superconductors. The latter, in particular, have drawn interest as a potential platform for quantum computing, in which information can be stored in a way that is intrinsically robust to random noise.The research focuses on two themes that are of current interest both for expanding our understanding of new types of possible quantum phenomena, and for investigating how strong interactions can potentially help identify promising platforms for quantum computing. The first theme is expanding our understanding of how topological properties can lead to new types of interacting quantum matter in three dimensions. The second theme is understanding how strong interactions, and ultimately the kinds of topological properties that are already well-understood in these systems, help shape how quantum systems evolve in time at finite temperature.The project will contribute to the workforce of highly trained STEM professionals both by training graduate students, and through programs and events coordinated by the PI focused on facilitating the transition of interested physics undergraduate and graduate students at the University of Minnesota to jobs in the private sector. This includes working with engineering departments to allow interested physics undergraduates to participate in senior engineering design projects, as well as helping coordinate extracurricular networking and career-information events aimed specifically at physics students.TECHNICAL SUMMARYThis award supports research and education towards understanding the role of topology and constraints in two areas: new phases of matter in three dimensions, and the dynamics of low-dimensional systems. In the area of phases of matter in three dimensions, the proposed research will focus on recently discovered fracton phases of matter, with the unusual feature that their low-lying excitations have restricted mobility. A combination of field-theoretic techniques and tools for analyzing group cohomology developed in the study of interacting symmetry-protected phases of matter will be used to address the following questions. First, what field theories exhibit the qualitative features of fracton phases? Second, when does symmetry in these and related systems lead to protected gapless boundary modes? Addressing these questions will expand our understanding of how the interplay between geometry and topology in these systems leads to physical properties qualitatively unlike those of other three-dimensional quantum phases.In the area of dynamics in low-dimensional systems, the focus will be on exploring the impact of constraints and topological order on dynamics. The proposed research will use a combination of numerical (exact diagonalization) and analytical approaches based in perturbation theory and random-matrix theory. As low-dimensional systems that approximate constrained systems become experimentally accessible, clarifying whether, when, and how constraints can lead to unusually slow dynamics in quantum many-body systems can significantly advance our understanding of how information can be more robustly stored at intermediate time-scales in quantum many-body systems. The project will contribute to the workforce of highly trained STEM professionals both by training graduate students, and through programs and events coordinated by the PI focused on facilitating the transition of interested physics undergraduate and graduate students at the University of Minnesota to jobs in the private sector. This includes working with engineering departments to allow interested physics undergraduates to participate in senior engineering design projects, as well as helping coordinate extracurricular networking and career-information events aimed specifically at physics students.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.