CAREER: Geometric Quantum Order: Fractons, Tensor Gauge Theories and Beyond

职业：几何量子阶：分形、张量规范理论及其他

• 批准号: 2045181
• 负责人: Andrey Gromov
• 金额: $ 57.46万
• 依托单位: Brown University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2021
• 资助国家: 美国
• 起止时间: 2021-07-01 至 2026-06-30
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2045181&HistoricalAwards=false
• 关键词: CAREER; Geometric; Quantum; Order; Fractons

NONTECHNICAL SUMMARYThis CAREER award supports joint theoretical research and education to advance the theoretical foundations of condensed matter physics. Condensed matter physics concerns itself with systems composed of a large number of interacting constituents. Materials are a common example as they contain many atoms and many electrons. It is common to think of such complex systems not in terms of the individual constituents, but rather in terms of properties that emerge from their collective behavior. The concept of phases of matter is an important example of a collective property. Systems that show the same phase have similar properties. Ferromagnets have the collective property that the constituent atoms or electrons align in such a way that the magnetic axis of each one points in the same direction. Ferromagnets made of different materials are all ferromagnets. However, a ferromagnet is qualitatively different from an antiferromagnetic phase in which the magnetic axis of one atom points in the direction opposite that of its neighbor. So, systems that belong to the same phase have similar qualitative properties, while systems that belong to different phases have different properties. When quantum mechanics mingles with strong interactions among constituents very strange phases can emerge, such as the topological phases of the fractional quantum Hall effect; the latter occurs when electrons confined to a two-dimension plane by semiconductors are exposed to an intense magnetic field.Recently proposed fracton phases of matter are another turning point in this development. These phases have the interesting and distinct property of being hypersensitive to the geometry of the underlying material, for example the way atoms are organized on a lattice, as well as the presence of geometric distortions of the lattice. The PI will undertake a careful study and characterization of these phases, which necessitates the development new concepts and new theoretical tools. New tools will help advance understanding of the physical properties of fracton phases as well as suggest routes for experimental detection of fractions in materials. This is fundamental research; however, fractons could play an important role in developing quantum memory, and suggest new ways to think about quantum computing. Finally, it is already becoming clear that some fracton phenomena may have been discovered long ago in superfluids and liquid crystals, without realizing that these are but a page of a much bigger story. The PI will utilize the new techniques developed in the fracton context to gain new insights into the problems of vortices in superconductors, turbulence, and quantum liquid crystals.The education component of this CAREER project includes training undergraduate and graduate students. Students will explore how to use machine learning methods to gain insight into theoretical problems. The PI will participate in global efforts to increase diversity in physics through mentoring undergraduate students who are members of underrepresented groups leveraging American Physical Society initiatives. The PI will engage in outreach in local high schools by participating in career days and encouraging students to study science. PI will develop a course aimed at undergraduate and graduate students that will focus on applications of condensed matter physics ideas to deep neural networks. TECHNICAL SUMMARYThis CAREER award supports joint theoretical research and education to advance the theoretical foundations of strongly correlated topological and geometric phases of matter. The project is focused on the physics of systems that support emergent fracton excitations. These excitations possess two remarkable properties: (i) they are topologically non-trivial and (ii) they cannot freely move through space. The constraints on their motion arise dynamically, while the underlying physical system is translation invariant. More concretely the research concentrated on three major efforts. (i) Fracton excitations can emerge in gapless correlated spin liquids. The PI will explore how the existence of these excitations affects observable properties of these systems. (ii) The constrained mobility of fracton excitations can be formally imposed by introducing additional symmetries. The variety of all possible mobility constraints roughly corresponds to all possible symmetries of this kind. The PI will develop a general theory of such symmetries and their manifestation in low energy properties of the physical systems constrained by these symmetries. (iii) A particular form of fracton behavior is already present in well-known systems such as superfluids, liquid crystals and quantum Hall states, where vortices, crystalline defects and composite fermions have a subtle version of constrained motion. The PI will investigate this tantalizing connection with the expectation that fracton machinery will provide a fresh look at these systems. The education component of this CAREER project includes training undergraduate and graduate students. Students will explore how to use machine learning methods to gain insight into theoretical problems. The PI will participate in global efforts to increase diversity in physics through mentoring undergraduate students who are members of underrepresented groups leveraging American Physical Society initiatives. The PI will engage in outreach in local high schools by participating in career days and encouraging students to study science. PI will develop a course aimed at undergraduate and graduate students that will focus on applications of condensed matter physics ideas to deep neural networks.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.

非技术总结这个职业奖支持联合理论研究和教育，以推进凝聚态物理的理论基础。凝聚态物理学关注的是由大量相互作用的成分组成的系统。材料是一个常见的例子，因为它们含有许多原子和许多电子。人们通常不从单个成分的角度来考虑这种复杂系统，而是从它们的集体行为中出现的属性来考虑。物质相的概念是集体属性的一个重要例子。显示相同相位的系统具有相似的性质。铁磁体具有这样的集体性质，即组成原子或电子的排列方式使得每个原子或电子的磁轴指向相同的方向。由不同材料制成的铁磁体都是铁磁体。然而，铁磁体与反铁磁相在性质上不同，反铁磁相中一个原子的磁轴指向与其相邻原子相反的方向。因此，属于同一阶段的系统具有相似的定性性质，而属于不同阶段的系统具有不同的性质。当量子力学与组分之间的强相互作用相结合时，可能会出现非常奇怪的相，例如分数量子霍尔效应的拓扑相;后者发生在电子被半导体限制在二维平面上时，暴露在强磁场中。最近提出的物质的分形相是这一发展的另一个转折点。这些相具有对底层材料的几何形状高度敏感的有趣和独特的性质，例如原子在晶格上的组织方式，以及晶格的几何畸变的存在。PI将对这些阶段进行仔细的研究和表征，这需要开发新的概念和新的理论工具。新的工具将有助于推进对分形相物理性质的理解，并为材料中分数的实验检测提供建议。这是基础研究;然而，分形子可以在开发量子存储器方面发挥重要作用，并为量子计算提供新的思路。最后，已经变得越来越清楚的是，一些分形现象可能很久以前就在超流体和液晶中发现了，而没有意识到这些只是一个更大的故事的一页。PI将利用在分形背景下开发的新技术，以获得对超导体，湍流和量子液晶中的涡旋问题的新见解。该职业项目的教育部分包括培训本科生和研究生。学生将探索如何使用机器学习方法来深入了解理论问题。PI将参与全球努力，通过指导本科生谁是代表性不足的群体利用美国物理学会的举措的成员，以增加物理学的多样性。PI将通过参加职业日和鼓励学生学习科学，在当地高中开展外联活动。PI将开发一门针对本科生和研究生的课程，重点关注凝聚态物理学思想在深度神经网络中的应用。该职业奖支持联合理论研究和教育，以推进物质的强相关拓扑和几何相的理论基础。该项目的重点是支持紧急fracton激发系统的物理学。这些激发具有两个显著的性质：（i）它们在拓扑上是非平凡的，（ii）它们不能在空间中自由移动。对它们运动的约束是动态产生的，而底层的物理系统是平移不变的。更具体地说，研究集中在三个主要方面。(i)分形子激发可以出现在无间隙的相关自旋液体中。PI将探索这些激励的存在如何影响这些系统的可观测特性。(ii)分形子激发的受约束的迁移率可以通过引入额外的对称性来正式施加。所有可能的迁移率约束的变化大致对应于所有可能的这种对称性。PI将发展这种对称性的一般理论，以及它们在受这些对称性约束的物理系统的低能性质中的表现。(iii)一种特殊形式的分形行为已经存在于众所周知的系统中，如超流体，液晶和量子霍尔态，其中涡旋，晶体缺陷和复合费米子具有受约束运动的微妙版本。PI将调查这一诱人的联系，并期望分形机械将为这些系统提供一个新的视角。这个职业项目的教育部分包括培训本科生和研究生。学生将探索如何使用机器学习方法来深入了解理论问题。PI将参与全球努力，通过指导本科生谁是代表性不足的群体利用美国物理学会的举措的成员，以增加物理学的多样性。PI将通过参加职业日和鼓励学生学习科学，在当地高中开展外联活动。PI将开发一门针对本科生和研究生的课程，重点关注凝聚态物理思想在深度神经网络中的应用。该奖项反映了NSF的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。

项目成果

Quantum Many-Body Topology of Quasicrystals

• DOI: 10.1103/physrevx.11.041051
• 发表时间: 2021-03
• 期刊: Physical Review X
• 影响因子: 12.5
• 作者: D. Else;Shengxun Huang;Abhinav Prem;A. Gromov

Critical Initialization of Wide and Deep Neural Networks through Partial Jacobians: General Theory and Applications

通过部分雅可比行列式对广度和深度神经网络进行关键初始化：一般理论和应用

• DOI: 10.48550/arxiv.2111.12143
• 发表时间: 2022
• 期刊: ArXivorg
• 作者: Doshi, Darshil;He, Tianyu;Gromov, Andrey
• 通讯作者: Gromov, Andrey