CAREER: Symmetry, Topology, and Transport in Strongly Interacting Quantum Many-Body Systems

职业：强相互作用量子多体系统中的对称性、拓扑和输运

基本信息

批准号：
1753240
负责人：
Maissam Barkeshli
金额：
$ 43.05万
依托单位：
University of Maryland, College Park
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-02-15 至 2024-01-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1753240&HistoricalAwards=false
关键词：
CAREER Symmetry Topology Transport Strongly

项目摘要

NONTECHNICAL SUMMARYThis CAREER award supports research and education on fundamental questions in quantum condensed matter systems and their applications to quantum computing. A central question in physics is to understand how matter can collectively organize itself into many different types of ordered phases. The transformation of water into ice is a common example. The study of liquids, crystals, magnets, superconductors, and other such phases of matter has revolutionized our understanding of matter itself and the technological basis of our society. The last decade has seen a renaissance in our ability to theoretically understand and experimentally probe novel quantum states of matter that do not exhibit conventional types of organization, but which are rather characterized by a subtler quantum topological order. The phenomena exhibited by these quantum states of matter can potentially be harnessed for a variety of quantum technologies, including quantum computers, which would be able to solve certain computational tasks exponentially more efficiently than classical computers. The theoretical tools to describe these phenomena are currently under rapid development and require basic advances. The PI and his group will pursue a multifaceted research program to tackle foundational theoretical questions, and to address the question of characterizing distinct possible quantum states of matter and their collective phenomena. These will then be pursued further in the context of specific materials and experimental settings. Finally, the theoretical insights gained will be applied to devise new ways of protecting delicate quantum states from their external environment, in order to advance the pursuit of scalable, fault-tolerant quantum computers. The research project has significant impact not only on the condensed-matter community, but also on high-energy physics, mathematics, quantum information, and potentially in industry in the area of quantum computing. The research will be carried out primarily with graduate students and postdoctoral scholars, whose training will benefit from the wide and advanced scope of the projects. The PI plans to also mentor undergraduate students to study these topics, and to maintain contact with the local K-12 community through a number of outreach activities organized by the Joint Quantum Institute and Physics Frontier Center at the University of Maryland, with the aim of increasing the participation of women and underrepresented minorities in STEM fields. TECHNICAL SUMMARYThis CAREER award supports research and education on fundamental questions in strongly interacting quantum many-body systems and their applications to quantum computing. Recent years have seen a renaissance in our ability to theoretically characterize and experimentally probe novel quantum states of matter and their excitations. This progress includes an understanding of new types of topological defects that can occur in strongly interacting fractionalized phases of matter. The universal properties of these defects are characterized within a recently been developed theoretical framework that incorporates the interplay of symmetry and topology in strongly interacting quantum liquids. The research focuses on the following main objectives:(1) Further developing the understanding of the physics of these new types of topological line- and point-defects and how they can be studied by using realistic model Hamiltonians, and be realized and probed experimentally in graphene fractional quantum Hall systems, and quantum spin-liquid materials. (2) Developing a comprehensive theoretical framework to characterize and describe symmetric topological phases of matter. The current theory must be extended to incorporate situations of physical interest, such as where the symmetries include space-time symmetries and can be anti-unitary and/or continuous, and also situations where the microscopic constituents are fermions. The ultimate goal is to develop a complete list of topological invariants that fully characterize strongly interacting topological quantum states of bosons and fermions with symmetry. An important aspect of this investigation will be to subsequently apply the insights gained to our understanding of quantum critical phenomena as well. (3) Developing applications of defects and symmetry-enriched topological states to quantum computation. Specifically, all scalable approaches to quantum error correction with local interactions rely heavily on topological states of matter for fault-tolerance and thus can benefit from the advances in our understanding of defects and symmetry in topological states. (4) Studying hydrodynamic thermal and electrical transport behavior in metallic and quantum critical systems. The research project has significant impact not only on the condensed-matter community, but also on high-energy physics, mathematics, quantum information, and potentially in industry in the area of quantum computing. The research will be carried out primarily with graduate students and postdoctoral scholars, whose training will benefit from the wide and advanced scope of the projects. The PI plans to also mentor undergraduate students to study these topics, and to maintain contact with the local K-12 community through a number of outreach activities organized by the Joint Quantum Institute and Physics Frontier Center at the University of Maryland, with the aim of increasing the participation of women and underrepresented minorities in STEM fields.

非技术摘要这一职业奖支持有关量子凝结物质系统中基本问题及其在量子计算中的应用的研究和教育。物理学中的一个核心问题是了解物质如何将自己集体组织为许多不同类型的有序阶段。水转化为冰是一个常见的例子。液体，晶体，磁铁，超导体和其他此类物质阶段的研究彻底改变了我们对物质本身和社会技术基础的理解。在过去的十年中，我们在理论上理解和实验探测了不表现出传统类型的组织的物质的新量子状态的能力是一种复兴，但它们的特征是微妙的量子拓扑顺序。这些物质量子状态所表现出的现象可能会用于包括量子计算机在内的各种量子技术，这些量子计算机将能够比古典计算机更有效地求解某些计算任务。描述这些现象的理论工具目前正在快速发展，需要基本进步。 PI和他的小组将追求一项多方面的研究计划，以解决基础理论问题，并解决表征物质及其集体现象的不同量子状态的问题。然后，将在特定材料和实验环境的背景下进一步追求这些问题。最后，获得的理论见解将用于设计新的方法来保护精致的量子状态免受外部环境的侵害，以促进追求可扩展的耐断层量子计算机的追求。该研究项目不仅对凝结的养殖社区产生了重大影响，而且对高能物理学，数学，量子信息以及量子计算领域的行业有可能产生重大影响。这项研究将主要由研究生和博士后学者进行，他们的培训将受益于项目的广泛和高级范围。 PI计划还计划指导本科生研究这些主题，并通过马里兰大学联合量子研究所和物理边境中心组织的许多外展活动与当地的K-12社区保持联系，目的是增加妇女和代表性少数群体在STEM领域的参与。技术摘要这一职业奖支持有关强烈互动量子多体系统及其在量子计算中的应用中的基本问题的研究和教育。近年来，我们在理论上表征和实验探测了物质及其激发的新量子状态的能力进行了复兴。这种进步包括对可能发生在物质的强烈相互作用的分数阶段中可能发生的新型拓扑缺陷的理解。这些缺陷的通用特性在最近开发的理论框架中表征，该框架结合了对称性和拓扑的相互作用，在强烈相互作用的量子液体中。该研究侧重于以下主要目标：（1）进一步发展对这些新型拓扑线和点 - 缺陷的物理学的理解，以及如何通过使用现实的模型汉密尔顿人来研究它们，并在实验中实现和探测石墨烯分数量子霍尔系统和量子自旋液体材料。（2）开发一个全面的理论框架来表征和描述物质的对称拓扑阶段。当前的理论必须扩展以纳入物理兴趣的情况，例如对称性包括时空对称性，并且可以是反对的和/或连续的，也可以是微观成分是费米子的情况。最终的目标是制定拓扑不变的完整列表，这些拓扑不变性列表完全表征了与对称性的玻色子和费米子的强烈相互作用的拓扑量子态。这项研究的一个重要方面将是随后将所获得的见解也应用于我们对量子关键现象的理解。（3）在量子计算中开发缺陷和富含对称性的拓扑状态的应用。具体而言，所有可扩展的与局部相互作用量子误差校正的方法在很大程度上都取决于物质的拓扑状态，因此可以从我们对拓扑状态缺陷和对称性的理解中受益。（4）研究金属和量子关键系统中的流体动力和电运输行为。该研究项目不仅对凝结的养殖社区产生了重大影响，而且对高能物理学，数学，量子信息以及量子计算领域的行业有可能产生重大影响。这项研究将主要由研究生和博士后学者进行，他们的培训将受益于项目的广泛和高级范围。 PI计划还计划指导本科生研究这些主题，并通过马里兰大学联合量子研究所和物理边境中心组织的许多外展活动与当地的K-12社区保持联系，目的是增加妇女和代表性少数群体在STEM领域的参与。