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.

非技术摘要该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，因为它们包含许多原子和许多电子。人们通常认为这种复杂的系统不是从单个组成部分的角度来考虑的，而是从其集体行为所产生的属性的角度来考虑的。物质相的概念是集体财产的一个重要例子。显示相同相位的系统具有相似的特性。铁磁体具有这样的集体特性：组成原子或电子以每个原子或电子的磁轴指向同一方向的方式排列。不同材料制成的铁磁体都是铁磁体。然而，铁磁体与反铁磁相有本质上的不同，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，属于同一相的系统具有相似的性质，而属于不同相的系统具有不同的性质。当量子力学与成分之间的强相互作用混合时，就会出现非常奇怪的相，例如分数量子霍尔效应的拓扑相；当电子被半导体限制在二维平面内并暴露在强磁场中时，就会发生后者。最近提出的物质的分形相是这一发展的另一个转折点。这些相具有有趣且独特的特性，即对底层材料的几何形状高度敏感，例如原子在晶格上的组织方式，以及晶格几何扭曲的存在。 PI将对这些阶段进行仔细研究和表征，这需要开发新概念和新理论工具。新工具将有助于加深对分形相物理性质的理解，并为材料中分形的实验检测提供建议。这是基础研究；然而，分形可以在开发量子存储器方面发挥重要作用，并提出思考量子计算的新方法。最后，人们已经越来越清楚，一些分形现象可能很久以前就在超流体和液晶中被发现，但没有意识到这些只是一个更大故事的一页。 PI 将利用在分形背景下开发的新技术来获得对超导体、湍流和量子液晶中的涡流问题的新见解。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 将利用美国物理学会的倡议，通过指导属于代表性不足群体的本科生，参与全球增加物理学多样性的努力。 PI 将通过参加职业日并鼓励学生学习科学来在当地高中进行推广。 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。技术摘要该职业奖支持联合理论研究和教育，以推进强相关的物质拓扑和几何相的理论基础。该项目的重点是支持紧急分形激发的系统物理学。这些激发具有两个显着的特性：（i）它们在拓扑上是不平凡的；（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，而底层物理系统是平移不变的。更具体地说，该研究集中在三项主要工作上。 (i) 分形子激发可以出现在无间隙相关自旋液体中。 PI 将探索这些激励的存在如何影响这些系统的可观察特性。 (ii) 分形激发的约束迁移率可以通过引入额外的对称性来形式化地施加。所有可能的移动性约束的多样性大致对应于这种类型的所有可能的对称性。 PI 将开发此类对称性的一般理论及其在受这些对称性约束的物理系统的低能量属性中的表现。 (iii) 一种特殊形式的分形行为已经存在于超流体、液晶和量子霍尔态等众所周知的系统中，其中涡流、晶体缺陷和复合费米子具有微妙的约束运动。 PI 将调查这种诱人的联系，期望 fracton 机械将为这些系统提供全新的视角。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 将利用美国物理学会的倡议，通过指导属于代表性不足群体的本科生，参与全球增加物理学多样性的努力。 PI 将通过参加职业日并鼓励学生学习科学来在当地高中进行推广。 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进行评估，被认为值得支持标准。

项目成果

Very-High-Energy Collective States of Partons in Fractional Quantum Hall Liquids

分数量子霍尔液体中部分子的极高能集体态

• DOI: 10.1038/s42005-021-00540-4
• 发表时间: 2022-04
• 期刊: Physical review
• 作者: Balram, Ajit C.;Liu, Zhao;Gromov, Andrey;Papić, Zlatko
• 通讯作者: Papić, Zlatko

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: 2022-01
• 期刊: ArXivorg
• 作者: Doshi, Darshil;He, Tianyu;Gromov, Andrey
• 通讯作者: Gromov, Andrey

Quantum Many-Body Topology of Quasicrystals

准晶体的量子多体拓扑

• DOI: 10.1103/physrevx.11.041051
• 发表时间: 2021-03-24
• 期刊: Physical Review X
• 影响因子: 12.5
• 作者: D. Else;Shengxun Huang;Abhinav Prem;A. Gromov
• 通讯作者: A. Gromov