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

非技术总结这个职业奖支持量子凝聚态系统及其在量子计算中的应用的基本问题的研究和教育。物理学的一个中心问题是理解物质如何集体地将自己组织成许多不同类型的有序相。水变成冰是一个常见的例子。对液体、晶体、磁体、超导体和物质的其他相态的研究彻底改变了我们对物质本身和我们社会的技术基础的理解。在过去的十年里，我们在理论上理解和实验上探索物质的新量子态的能力得到了复兴，这些量子态不表现出传统的组织类型，而是以更微妙的量子拓扑秩序为特征。这些物质量子态所表现出的现象可能被用于各种量子技术，包括量子计算机，它将能够比经典计算机更有效地解决某些计算任务。描述这些现象的理论工具目前正在迅速发展，需要基本的进步。PI和他的团队将开展多方面的研究计划，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可能量子态的问题。然后将在具体材料和实验环境的背景下进一步探讨这些问题。最后，所获得的理论见解将被应用于设计新的方法来保护微妙的量子态免受外部环境的影响，以推动对可扩展的容错量子计算机的追求。该研究项目不仅对凝聚态社区产生了重大影响，而且对高能物理，数学，量子信息以及量子计算领域的潜在工业也产生了重大影响。研究将主要与研究生和博士后学者一起进行，他们的培训将受益于项目的广泛和先进范围。PI还计划指导本科生学习这些主题，并通过马里兰州大学联合量子研究所和物理前沿中心组织的一些外展活动与当地K-12社区保持联系，目的是增加妇女和代表性不足的少数民族在STEM领域的参与。该职业奖支持强相互作用量子多体系统及其在量子计算中的应用的基础问题的研究和教育。近年来，我们在理论上表征和实验上探测物质的新量子态及其激发的能力得到了复兴。这一进展包括对新型拓扑缺陷的理解，这些缺陷可能发生在物质的强烈相互作用的分馏阶段。这些缺陷的普遍性质的特点是在最近开发的理论框架，结合强相互作用的量子液体的对称性和拓扑结构的相互作用。本研究的主要目标是：（1）进一步发展对这些新型拓扑线缺陷和点缺陷的物理理解，以及如何使用现实模型哈密顿量来研究它们，并在石墨烯分数量子霍尔系统和量子自旋液体材料中实现和实验探索。(2)发展一个全面的理论框架来表征和描述物质的对称拓扑相。目前的理论必须扩展到包含物理意义的情况，例如对称性包括时空对称性，并且可以是反酉和/或连续的，以及微观成分是费米子的情况。最终的目标是发展一个完整的拓扑不变量列表，充分表征强相互作用的玻色子和费米子的拓扑量子态的对称性。这项研究的一个重要方面将是随后将获得的见解应用于我们对量子临界现象的理解。(3)量子计算中的缺陷和拓扑态的应用。具体来说，所有可扩展的方法，以量子纠错与本地相互作用严重依赖于容错的拓扑状态的物质，因此可以受益于我们的理解的缺陷和对称性的拓扑状态的进步。(4)研究金属和量子临界系统中的流体动力学热和电输运行为。该研究项目不仅对凝聚态社区产生了重大影响，而且对高能物理，数学，量子信息以及量子计算领域的潜在工业也产生了重大影响。研究将主要与研究生和博士后学者一起进行，他们的培训将受益于项目的广泛和先进范围。PI还计划指导本科生学习这些主题，并通过马里兰州大学联合量子研究所和物理前沿中心组织的一些外展活动与当地K-12社区保持联系，目的是增加妇女和代表性不足的少数民族在STEM领域的参与。

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.