Exploring Phases of Matter With Restrictive Conservation Laws: Anomalies, Topology, and Dynamics

非技术总结该奖项支持理论研究，总体目标是了解多粒子量子系统中的约束如何导致物质和物理现象的新阶段。在过去的十年里，新的实验使得对物理机制的研究成为可能，在这种机制中，许多粒子共同合作，以与单个原子表现出的行为截然不同的方式共同行动。这使得物理学家能够探索一系列有趣的现象，从合成奇异的新型粒子，到实现可以在任意长时间内记住其初始状态的物质状态(与热力学定律的预测形成鲜明对比)。这些新的实验能力重新努力了解量子多体系统中可能出现什么样的集体行为。了解这些可能性既对扩大我们对周围世界的理解具有基本意义，也有可能在推进量子计算方面产生实际影响。该项目的一个部分重点是探索一类新的此类行为，当微观粒子经历某种限制的运动时，可能会出现这种行为，目的是开发新的数学工具和框架来描述它们。这样的框架将使人们能够更广泛地探索这些迁移率限制可能导致的新类型的物理效应，包括它们在受保护的量子态中存储量子信息的潜力，这些量子态在空间上位于边界附近。推动这一新一代实验前沿的一个主要挑战是噪声：将量子系统与其环境耦合的随机过程，最终摧毁存储在其中的微妙量子信息。因此，理解复杂的多体量子系统中的噪声已成为一个日益重要的问题。该项目的第二部分侧重于了解对粒子迁移率的限制，以及可以对量子系统施加的相关限制，如何影响某些类型的噪声的影响。这项研究的目的是了解这种约束是否以及何时会导致对噪声出人意料地强大的量子现象。该奖项还将支持国际量子学院的教育和推广活动，包括：(I)将本科生量子力学课程现代化，并将由国际量子研究所设计的关于量子计算和量子信息的专题课程过渡到常规课程，(Ii)培训研究生基本分析和数值技能，以及(Iii)帮助协调旨在吸引女性和少数族裔进入物理学专业的活动。技术总结该奖项支持理论研究，总体目标是了解多粒子量子系统中的限制如何导致新的物质相和物理现象。将调查两类问题。第一个是理解拓扑和高度约束的对称性之间的相互作用，比如子系统对称性，它需要粒子运动来守恒所有的多极矩。PI将(I)探索如何使用子系统对称性中的异常来理解文献中已知的不同类别的无间隙边界模式，以及(Ii)应用新的数学工具来研究一种被称为拓扑缺陷网络的一般结构，该结构可以在2维中产生大量的子系统对称模型。这项研究也可能对理解对称性约束不那么严格的相有意义，例如守恒的偶极(但不是更高的多极)矩，这可能会导致实验上可验证的预测，例如，在一些冷原子系统中自然产生全局偶极对称性。要探索的第二类问题是约束如何影响开放量子系统的动力学。一个特别的重点是理解什么时候会出现慢动力学，这样量子相干性就可以保持出人意料的长时间。在这里，PI将通过为具有局部约束的Hilbert空间开发一种改进的Lindblad形式来探索约束对动力学的影响。这种形式主义可用于研究开放系统动力学，在各种情况下，约束可导致非典型哈密顿动力学，如希尔伯特空间破碎和近似量子疤痕。该奖项还将支持PI的教育和推广活动，包括(I)使本科生量子力学课程现代化，并将PI设计的关于量子计算和量子信息的专题课程转变为常规课程，(Ii)培训研究生基本分析和数值技能，以及(Iii)帮助协调旨在吸引女性和少数族裔获得物理学硕士学位的活动。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势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 theoretical research with a general goal to understand how constraints in many-particle quantum systems can lead to novel phases of matter and physical phenomena. During the last decade, new experiments have enabled the study of regimes of physics, in which many particles conspire to behave collectively in ways that are very different from the behaviors exhibited by individual atoms. This has allowed physicists to explore a wide range of intriguing phenomena, from synthesizing exotic new kinds of particles, to realizing states of matter that can remember their initial state for an arbitrarily long time (in sharp contrast to the predictions of the laws of thermodynamics).These new experimental capabilities have renewed efforts to understand what kinds of collective behaviors can emerge in quantum many-body systems. Understanding these possibilities has both fundamental implications for expanding our understanding of the world around us, and the potential for practical implications in advancing quantum computing. One part of this project focuses on exploring a new class of such behaviors, that can arise when the microscopic particles undergo motion that is restricted in some way, with the aim of developing new mathematical tools and frameworks to describe them. Such frameworks will enable a more general exploration of what new kinds of physical effects these mobility restrictions can lead to, including their potential for storing quantum information in protected quantum states that are spatially localized near their boundaries. A major challenge in pushing the frontiers of this new generation of experiments is noise: random processes that couple a quantum system to its environment, ultimately destroying the delicate quantum information stored therein. As such, understanding noise in complex, many-body quantum systems has become an increasingly important problem. The second part of this project focuses on understanding how restrictions on particle mobility, as well as related constraints that can be imposed on quantum systems, affect the impact of certain types of noise. The goal of this study is to understand whether, and when, such constraints can lead to quantum phenomena that are unexpectedly robust to noise.This award will also support the PI's education and outreach activities, which consist of (i) modernizing the undergraduate quantum mechanics curriculum and transitioning a special topics course on quantum computation and quantum information designed by the PI to a regular course, (ii) training graduate students in both basic analytical and numerical skills, and (iii) helping coordinate events aimed at attracting women and minorities to the physics major.TECHNICAL SUMMARYThis award supports theoretical research with a general goal to understand how constraints in many-particle quantum systems can lead to novel phases of matter and physical phenomena. Two classes of problems will be investigated. The first consists of understanding the interplay between topology and highly constraining symmetries, such as subsystem symmetry, which requires particle motion to conserve all multipole moments. The PI will (i) explore how anomalies in subsystem symmetries can be used to understand different classes of gapless boundary modes that are known in the literature, and (ii) apply new mathematical tools to study a general construction, known as a topological defect network, that can produce a wide array of subsystem-symmetric models in 2 dimensions. This research may also have implications for understanding phases with less stringent symmetry constraints, such as conserved dipole (but not higher multipole) moments, that may lead to experimentally verifiable predictions, as global dipole symmetry arises naturally, for example, in some cold atomic systems. The second class of questions to be explored is how constraints impact the dynamics of open quantum systems. A particular focus is on understanding when slow dynamics can arise, such that quantum coherence can be preserved for an unexpectedly long time. Here, the PI will explore the impact of constraints on dynamics by developing a modified Lindblad formalism for Hilbert spaces with local constraints. This formalism can be used to study open system dynamics in a variety of cases where constraints are known to lead to atypical Hamiltonian dynamics, such as Hilbert space shattering and approximate quantum scars.This award will also support the PI's education and outreach activities, which consist of (i) modernizing the undergraduate quantum mechanics curriculum and transitioning a special topics course on quantum computation and quantum information designed by the PI to a regular course, (ii) training graduate students in both basic analytical and numerical skills, and (iii) helping coordinate events aimed at attracting women and minorities to the physics major.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.