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

本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，其相互作用强烈或仅在强电子相互作用的存在下出现。最近发现了一种新的物质状态，称为拓扑绝缘体，它引起了极大的兴奋，并导致了凝聚态物理学的许多革命性发展。拓扑绝缘子的一个重要特征是其特有的输运性质。固体中电子的通常输运现象（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无耗散的量子输运通过它们的边界，同时在整体中保持绝缘。这种拓扑起源的量子输运现象是低能量成本的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有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的数量级。虽然非相互作用和无无序拓扑绝缘体已经被很好地理解，但下一个重要的挑战是理解强相互作用或仅在强电子相互作用存在下才出现的物质的拓扑相。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斥力强烈地相互作用，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将寻找可能以新的拓扑现象为特征的新颖的、完全相互作用的物质相。该项目的研究活动本质上是跨学科的，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，并可能进一步与具体的数值模拟和凝聚态系统的实验联系起来。来自凝聚态物质、材料科学、高能物理和数学等不同背景的学生和青年研究人员将参与研究活动。他们将被培养成新一代的研究人员，能够在未来跨学科和跨学科工作。特别是，计划以美国和日本的青年科学家为对象，举办以拓扑现象为主题的研习班和暑期学校。本职业奖支持探索物质拓扑相的理论研究，这些拓扑相是强相互作用的，或者只有在强电子相互作用的存在下才会出现。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的拓扑相，这些相可能以新的拓扑现象为特征。在这个项目中采取的攻击路线是使用量子异常，即通过量子效应破坏对称性，来描述和诊断相互作用的拓扑相，可能受到一些对称性的保护。更具体地说，本项目旨在：1)推广劳克林的思想实验，这是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稳性，以适用于更广泛的拓扑相，例如受对称性保护的拓扑相和缺乏粒子数守恒的拓扑相。2)利用量子异常构造有效作用，发展相互作用的拓扑绝缘体和拓扑超导体集体动力学的流体力学有效场论描述。3)建立拓扑绝缘子中电子位置算子服从的反常对易关系（坐标非对易性）与相互作用拓扑绝缘子的集体动力学之间的联系。该项目的研究活动本质上是跨学科的，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，并可能进一步与具体的数值模拟和凝聚态系统的实验联系起来。来自凝聚态物质、材料科学、高能物理和数学等不同背景的学生和青年研究人员将参与研究活动。他们将被培养成新一代的研究人员，能够在未来跨学科和跨学科工作。特别是，计划以美国和日本的青年科学家为对象，举办以拓扑现象为主题的研习班和暑期学校。

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.