CAREER: "Geometry, topology and symmetry in strongly correlated materials"

非技术性总结这个职业奖支持理论研究和教育，旨在研究某些称为拓扑相的材料的性质。这些是物质的状态，与大多数其他物质不同，它们具有坚固的物理特性，不受变形和杂质的影响。这导致了一些拓扑相可以被有益地用于存储信息并以今天的计算机中不可能的方式操纵其流动的可能性。到目前为止，大多数可能适合这些应用的材料都是在普通条件下很难实现的条件下设计的;它们需要非常高的磁场和非常低的温度。PI将进行理论研究，旨在更好地了解承载电子拓扑相的材料的物理特性，并探索在没有大磁场的情况下最有利于实现拓扑相的条件。鲁棒性的现象类似于那些发生在电子拓扑相位也预测发生在系统中的定期外部扰动的作用。PI旨在更好地理解这些行为，并对可能的行为类型进行分类。这项研究可能有助于最终在计量学和计算中的有用应用，并可能有助于开发和改进开源量子多体计算机程序。PI将与洛杉矶的加州大学现有的外展计划合作，将新的实验引入大学预科课程。PI将利用现有的“本科生研究经验”计划，让本科生参与研究，并通过克莱尔布斯吕斯基金会建立女学生对物理学的兴趣。PI将继续开发有关拓扑现象的课程材料，并通过介绍性演讲和期刊俱乐部帮助传播新思想。该职业奖支持强相关系统的理论研究和教育，重点关注几何，对称性和拓扑结构之间的相互作用。拓扑相超出了通过对称性组织相的传统范式;然而，它们凭借其新颖的电子性质，具有实现新器件技术和实现量子计算的潜力。为了促进对拓扑相位的理解，PI将重点关注以下方面：1）发展分数量子霍尔效应与分数陈式绝缘体的统一理论。通过在这些系统中结合单粒子希尔伯特空间的量子几何学方面，PI建议设计和开发新的分析和数值工具，这些工具应该有助于寻找更多实验上可实现的量子霍尔现象。2.）研究晶体对称性在拓扑现象中的作用。利用拓扑参数，PI计划改进对称性强制简并的约束，并完成具有晶体对称性的短程纠缠拓扑态的分类。3.）第三章探索周期性驱动系统中的拓扑现象。PI的目标是描述这些拓扑鲁棒现象，研究相互作用的影响，分类的物理后果，并将这些与实验联系起来。PI的教育和推广活动将促进多样性，改善小学、本科和研究生的科学教育。PI将与加州大学洛杉矶现有的外展计划合作，为大学预科课程引入新的实验。PI将通过现有的“本科生研究经验”项目让本科生参与暑期研究项目，并通过克莱尔布斯吕斯基金会培养女学生对物理学的兴趣。PI将继续开发有关拓扑现象的课程材料。正在进行的研究的新发展将通过介绍性谈话和杂志俱乐部传播。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education aimed to study the properties of certain materials called topological phases. These are states of matter which unlike most others have physical properties that are robust and are not affected by deformation and impurities. This leads to the possibility that some topological phases can be profitably used to store information and manipulate its flow in ways that are not possible in today's computers. Most kinds of materials that might lend themselves to these applications have so far been engineered in conditions which are quite hard to achieve under ordinary conditions; they require very high magnetic fields and very low temperatures. The PI will perform theoretical research aimed to understand better the physics of the materials that host topological phases of electrons and to explore the conditions that most favor the realization of topological phases in the absence of large magnetic fields. Robust phenomena similar to those that occur in electronic topological phases are also predicted to occur in systems which are acted on by a periodic external perturbation. The PI aims to understand these better and to classify the types of behavior that are possible. This research may contribute to eventual useful applications in metrology and in computation, and may help develop and improve open source quantum many-body computer programs. It could also lead to the development of new photonic devices.The PI will work with existing outreach programs at University of California, Los Angeles to introduce new experiments to the pre-collegiate curriculum. The PI will tap into an existing "Research Experience for Undergraduates" program to involve undergraduate students in research and build interest in physics among female students through the Clare Booth Luce foundation. The PI will continue development of course materials on topological phenomena and also help in dissemination of new ideas through introductory talks and a journal club. TECHNICAL SUMMARYThis CAREER award supports theoretical research and education on strongly correlated systems focusing on the interplay among geometry, symmetry and topology. Topological phases lie outside the conventional paradigm of organizing phases by symmetry; nevertheless, they hold potential for enabling new device technologies and realizing quantum computation by virtue of their novel electronic properties. To advance understanding of topological phases, the PI will focus on the following thrusts: 1.) Developing a unified theory of the fractional quantum Hall effect and fractional Chern insulators. By incorporating aspects of the quantum geometry of the single particle Hilbert space in these systems, the PI proposes to design and develop new analytic and numerical tools which should aid the search for more experimentally accessible realizations of quantum Hall phenomena. 2.) Investigating the role of crystal symmetries in topological phenomena. Using topological arguments, the PI plans to improve constraints on symmetry enforced degeneracies and complete the classification of short-range entangled topological states with crystal symmetries. 3.) Exploring topological phenomena in periodically driven systems. The PI will aim to characterize these topologically robust phenomena, study the effects of interactions, the physical consequences of the classification, and connect these with experiments. The PI's education and outreach activities will promote diversity and improve science education at the elementary, undergraduate and graduate levels. The PI will work with existing outreach programs at the University of California, Los Angeles to introduce new experiments to the pre-collegiate curriculum. The PI will involve undergraduates in summer research programs through an existing "Research Experience for Undergraduates" program and build interest in physics among female students through the Clare Booth Luce foundation. The PI will continue developing course materials on topological phenomena. New developments in ongoing research will be disseminated through introductory talks and a journal club.