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

非技术总结这个职业奖支持理论研究，探索凝聚态物质的奇异量子力学相，称为拓扑相，它们相互作用强烈或仅在存在强电子相互作用的情况下出现。最近发现了一种新的物质状态，称为拓扑绝缘体，引起了极大的兴奋，并导致了凝聚态物理学的许多革命性发展。拓扑绝缘体的关键特征之一与其独特的输运性质有关。电子在固体中的物质输运现象（电流的流动）伴随着耗散（焦耳热）。 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输运，同时保持体绝缘。 这种拓扑起源的量子输运现象是低能耗电子学和自旋电子学的有希望的候选者。拓扑介质中的激发也被期望为量子计算提供一个有前途的平台，在计算速度方面可以超过其经典对应物几个数量级。虽然非相互作用和无无序拓扑绝缘体被合理地很好地理解，下一个重要的挑战是要理解强相互作用或只在强电子存在时才出现的物质的拓扑相交互. 这是本项目所追求的研究主题。 固体中的电子可以通过库仑排斥相互作用，这种强烈的相互作用有时会导致奇异的，意想不到的物质形式。通过发展新的理论方法，PI将寻找新的、完全相互作用的物质相，这些相可能具有新的拓扑现象。该项目的研究活动是跨学科的，旨在促进凝聚态理论与其他学术领域之间的相互作用，如高能物理，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和凝聚态系统的实验。来自凝聚态、材料科学、高能物理和数学等不同背景的学生和年轻研究人员将参与研究活动。他们将被培训为新一代的研究人员，他们将能够在未来跨学科和跨学科工作。特别是，PI将为来自美国和日本的年轻科学家组织关于拓扑现象的研讨会和暑期学校。该职业奖支持探索物质拓扑相的理论研究，这些相是强相互作用的，或者只在存在强电子相互作用的情况下才出现。通过开发新的理论方法，PI将寻找新的，完全相互作用的拓扑相的物质，可能是新的拓扑现象的特点。在这个项目中采取的一系列攻击是使用量子异常，即量子效应对对称性的破坏，来描述和诊断相互作用的拓扑相位，可能受到某种对称性的保护。更具体地说，该项目旨在：1）概括劳克林的思想实验，最强大的理论工具之一，它建立了量子霍尔效应对无序和相互作用的极端鲁棒性，以适用于更广泛的拓扑相的方式，例如受对称性保护的拓扑相和缺乏粒子数守恒的拓扑相。利用量子反常来建构有效作用量，并发展相互作用拓扑绝缘体与拓扑超导体集体动力学的流体动力学有效场论描述。3)建立拓扑绝缘体中出现的电子位置算符（坐标非对易性）服从的异常对易关系与相互作用拓扑绝缘体的集体动力学之间的联系。 该项目的研究活动具有跨学科性质，旨在促进凝聚态理论与其他学术领域（如高能物理，计算物理，数学和材料科学）之间的相互作用。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和凝聚态系统的实验。来自凝聚态、材料科学、高能物理和数学等不同背景的学生和年轻研究人员将参与研究活动。他们将被培训为新一代的研究人员，他们将能够在未来跨学科和跨学科工作。特别是，PI将为来自美国和日本的年轻科学家组织关于拓扑现象的研讨会和暑期学校。

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.