CAREER: Quantum anomalies and collective dynamics in symmetry-protected topological phases

职业：对称保护拓扑相中的量子异常和集体动力学

• 批准号: 1455296
• 负责人: Shinsei Ryu
• 金额: $ 45万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-04-01 至 2019-11-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1455296&HistoricalAwards=false
• 关键词: CAREER; Quantum; anomalies; collective; dynamics

NON-TECHNICAL SUMMARYThis CAREER award supports theoretical research that explores exotic quantum mechanical phases of condensed matter, called topological phases, which interact strongly or arise only in the presence of strong electron interactions. The recent discovery of a new state of matter, called the topological insulator, has created great excitement and led to a number of revolutionary developments in condensed matter physics. One of the key features of topological insulators is related to their peculiar transport properties. Usual transport phenomena of electrons (the flow of an electric current) in solids are accompanied with dissipation (Joule heating). Topological states of matter, on the other hand, can support dissipation-free quantum transport through their boundaries while remaining insulating in the bulk. Such quantum transport phenomena of topological origin are promising candidates for electronics and spintronics with low energy cost. Excitations in topological media have also been expected to provide a promising platform for quantum computation that could outperform its classical counterpart by orders of magnitude in terms of computational speed.While non-interacting and disorder-free topological insulators are reasonably well understood, an important next challenge is to understand topological phases of matter that are strongly interacting or that arise only in the presence of strong electron interactions. This is the research theme that is pursued in this project. Electrons in solids can interact with each other strongly through the Coulomb repulsion, and this strong interaction can sometimes lead to exotic, unexpected forms of matter. By developing new theoretical approaches, the PI will search for novel, fully interacting phases of matter that may be characterized by new topological phenomena.The research activities in this project are interdisciplinary in nature and designed to stimulate interactions between condensed matter theory and other fields of academia, such as high-energy physics, computational physics, mathematics, and materials science. Success in these projects will impact many areas of theoretical physics, and may further connect to concrete numerical simulations and to experiments in condensed matter systems. Students and young researchers from various backgrounds, including condensed matter, materials science, high-energy physics, and mathematics will be integrated into the research activities. They will be trained as a new generation of researchers who will be able to work across and between disciplines in the future. In particular, the PI will organize workshops and summer schools for young scientists from the U.S. and Japan on the topic of topological phenomena. TECHNICAL SUMMARYThis CAREER award supports theoretical research that explores topological phases of matter, which are strongly interacting or which arise only in the presence of strong electron interactions. By developing new theoretical approaches, the PI will search for novel, fully interacting topological phases of matter that may be characterized by new topological phenomena. A line of attack taken in this project is to use quantum anomalies, i.e. breakdowns of symmetries by quantum effects, to describe and diagnose interacting topological phases, possibly protected by some symmetry. More specifically, this project aims to: 1) Generalize Laughlin's thought experiment, one of the most powerful theoretical tools, which establishes the extreme robustness of the quantum Hall effect against disorder and interactions, in the way it is applicable to a wider range of topological phases, such as topological phases protected by symmetries and topological phases that lack particle number conservation.2) Use quantum anomalies to construct effective actions and to develop hydrodynamic effective field theory descriptions of collective dynamics of interacting topological insulators and topological superconductors. 3) Establish a connection between anomalous commutation relations obeyed by electron position operators (the coordinate non-commutativity) that arise in topological insulators and collective dynamics of interacting topological insulators. The research activities in this project are interdisciplinary in nature and designed to stimulate interactions between condensed matter theory and other fields of academia, such as high-energy physics, computational physics, mathematics, and materials science. Success in these projects will impact many areas of theoretical physics, and may further connect to concrete numerical simulations and to experiments in condensed matter systems. Students and young researchers from various backgrounds, including condensed matter, materials science, high-energy physics, and mathematics will be integrated into the research activities. They will be trained as a new generation of researchers who will be able to work across and between disciplines in the future. In particular, the PI will organize workshops and summer schools for young scientists from the U.S. and Japan on the topic of topological phenomena.

非技术摘要这一职业奖支持理论研究，该研究探讨了凝结物质的外来量子机械阶段，称为拓扑阶段，拓扑阶段仅在存在强电子相互作用的情况下强烈相互作用或出现。最近发现的新物质（称为拓扑绝缘子）引起了极大的兴奋，并导致了许​​多革命性物理物理学的革命性发展。拓扑绝缘子的关键特征之一与其特殊的运输特性有关。固体中电子的通常运输现象（电流的流动）伴随着耗散（焦耳加热）。 另一方面，物质的拓扑状态可以支持通过其边界的无耗散量子传输，同时保持体积绝缘。 这种拓扑来源的量子运输现象是低能成本的电子和旋转基质的有希望的候选者。还期望拓扑媒体中的激发为量子计算提供一个有前途的平台，在计算速度方面，通过数量级来胜过其经典的同行。虽然非交互和无混乱的拓扑绝缘子是相当理解的，但接下来很重要，接下来很重要挑战是了解强烈相互作用或仅在存在强电子相互作用的情况下出现的物质的拓扑阶段。 这是该项目所追求的研究主题。 固体中的电子可以通过库仑排斥力强烈相互作用，这种强烈的相互作用有时会导致异国情调的意外物质形式。通过开发新的理论方法，PI将寻找可能以新的拓扑现象为特征的物质的新颖，完全相互作用的阶段。该项目的研究活动本质上是跨学科的，旨在刺激凝结物质理论与其他领域之间的相互作用学术界，例如高能物理学，计算物理，数学和材料科学。这些项目的成功将影响理论物理的许多领域，并可能进一步连接到具体的数值模拟以及在凝结物质系统中的实验。来自各种背景的学生和年轻研究人员，包括凝结物质，材料科学，高能物理学和数学，将纳入研究活动。他们将被培训为新一代的研究人员，他们将来能够在学科之间和在学科之间工作。特别是，PI将在拓扑现象的主题上为来自美国和日本的年轻科学家组织研讨会和暑期学校。技术摘要这一职业奖支持理论研究，探讨了物质的拓扑阶段，这些阶段是强烈相互作用或仅在存在较强的电子相互作用的情况下出现的。通过开发新的理论方法，PI将搜索可能以新的拓扑现象为特征的物质的新颖，完全相互作用的拓扑阶段。该项目采取的攻击线是使用量子异常，即通过量子效应对对称性的崩溃来描述和诊断相互作用的拓扑阶段，可能受到某些对称性的保护。更具体地说，该项目的目的是：1）概括Laughlin的思想实验，这是最强大的理论工具之一，它建立了量子厅效应对混乱和互动的极端鲁棒性，其方式适用于更广泛的拓扑范围阶段，例如受对称性和缺乏粒子数保护的拓扑阶段保护的拓扑阶段。2）使用量子异常来构建有效的作用，并开发相互作用拓扑绝缘子和拓扑超导体的集体动力学的流体动力学有效的现场理论描述。 3）建立在拓扑绝缘子中出现的电子位置操作员遵守的异常换向关系（坐标）与相互作用拓扑绝缘子的集体动力学之间的联系。 该项目中的研究活动本质上是跨学科的，旨在刺激凝结物质理论与学术界其他领域之间的相互作用，例如高能物理学，计算物理学，数学和材料科学。这些项目的成功将影响理论物理的许多领域，并可能进一步连接到具体的数值模拟以及在凝结物质系统中的实验。来自各种背景的学生和年轻研究人员，包括凝结物质，材料科学，高能物理学和数学，将纳入研究活动。他们将被培训为新一代的研究人员，他们将来能够在学科之间和在学科之间工作。特别是，PI将在拓扑现象的主题上为来自美国和日本的年轻科学家组织研讨会和暑期学校。