CAREER: Theoretical Investigation of Interacting Topological States of Matter

职业：物质相互作用拓扑态的理论研究

• 批准号: 1151786
• 负责人: Xiaoliang Qi
• 金额: $ 40.58万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2017-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1151786&HistoricalAwards=false
• 关键词: CAREER; Theoretical; Investigation; Interacting; Topological

TECHNICAL SUMMARYThis CAREER award supports theoretical research and education to systematically investigate interacting topological states of matter. In recent years, a systematical understanding has been obtained for non-interacting topological states of matter in generic symmetry classes. However, interacting topological states of matter are much less understood, and novel physical phenomena such as quantum number fractionalization are expected to occur, as has been learned from fractional quantum Hall states. The PI plans to systematically characterize interacting topological states of matter in different dimensions and symmetry classes, through a combination of three approaches:i) Construction and characterization of many-body ground state wavefunctions. The many-body ground state wavefunction provides a complete description of the ground state properties. The PI plans to generalize the wavefunction approach to fractional quantum Hall states, and construct ground state wavefunctions and corresponding model Hamiltonians of two-dimensional and three-dimensional topological states. ii) Topological field theory description. Topological field theory describes topological states by their observable physical properties. The PI aims to develop new topological field theories for topological states especially for topological superconductors. iii) Quantum entanglement properties of topological states and their relation to dynamical properties of the system. The PI will study the entanglement spectrum of topological states and also develop new characteristics of quantum entanglement properties.The proposed research will be integrated with education of graduate and undergraduate students. This project will provide graduate students with a unique research experience involving both solid training in theoretical condensed matter physics and a broad view of many related fields. The PI will make sustained efforts to introduce the proposed research to undergraduate students through lectures, classes and research projects. The PI has been active in organizing tutorials and workshops, writing review articles and pedagogical articles to benefit both junior and senior members of the community, and to introduce research results on topological states of matter to a broader audience. The PI plans to prepare public lectures on topological physics to disseminate the research results of this project and to attract broader interest in this subject beyond the physics community.NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education to systematically investigate topological states of matter involving electrons that interact strongly with each other. The first topological states of matter discovered are the quantum Hall effects which arise in electrons trapped in two dimensional sheets that are exposed to a large perpendicular magnetic field. A new topological state is the topological insulator. Like ordinary insulators, for example rubber, topological insulators do not conduct electricity through the interior of the material. Unlike ordinary insulators, topological insulators are able to conduct electricity on their edges or boundaries through the formation of a new state of matter. Among the known topological insulators are compounds made of the elements bismuth and selenium, and bismuth and tellurium.The PI aims to study the effect of the correlated motion of electrons that arise from strong interactions between electrons in topological states of matter. The current understanding of topological insulators largely neglects correlations. The PI aims to systematically characterize interacting topological states from several complimentary aspects. Correlations may lead to the discovery of new states of matter with properties that may be exploited for device applications. The PI will study the properties and the quanutm mechanical structure of these states. The PI will propose experimentally observable signatures of new topological states that qualitatively from familiar well understood states of matter. The proposed research will be integrated with education of graduate and undergraduate students. The PI will make sustained efforts to introduce the proposed research to undergraduate students through lectures, classes and research projects. The PI has been active in organizing tutorials and workshops, communicating science to benefit both junior and senior members of the community, introducing the research results on topological states of matter to a broader audience. The PI will prepare public lectures on topological physics to disseminate the research results of this project and to attract broader interest in this subject beyond the physics community.

该职业奖支持理论研究和教育，以系统地调查物质的相互作用拓扑状态。近年来，人们对一般对称类中物质的非相互作用拓扑状态有了较为系统的认识。然而，物质的相互作用拓扑状态的理解要少得多，并且新的物理现象，如量子数分数化，预计会发生，正如从分数量子霍尔态中学到的那样。PI计划通过三种方法的结合，系统地表征不同维度和对称类物质的相互作用拓扑状态：i)构建和表征多体基态波函数。多体基态波函数提供了基态性质的完整描述。PI计划将波函数方法推广到分数量子霍尔态，并构建二维和三维拓扑态的基态波函数和相应的模型哈密顿量。ii)拓扑场论描述。拓扑场论用可观察到的物理性质来描述拓扑态。该项目旨在为拓扑态特别是拓扑超导体发展新的拓扑场理论。iii)拓扑态的量子纠缠特性及其与系统动力学特性的关系。PI将研究拓扑态的纠缠谱，并开发量子纠缠特性的新特征。建议的研究将与研究生和本科生的教育相结合。该项目将为研究生提供一个独特的研究经验，包括理论凝聚态物理的扎实训练和许多相关领域的广阔视野。PI将持续努力，通过讲座、课程和研究项目向本科生介绍拟议的研究。PI一直积极组织教程和研讨会，撰写评论文章和教学文章，以使社区的初级和高级成员受益，并向更广泛的受众介绍物质拓扑状态的研究成果。PI计划准备有关拓扑物理学的公开讲座，以传播该项目的研究成果，并吸引物理界以外的更广泛的兴趣。该职业奖支持理论研究和教育，以系统地研究涉及相互强烈相互作用的电子的物质的拓扑状态。物质的第一个拓扑状态被发现是量子霍尔效应，它产生于被困在二维薄片中的电子，暴露在一个巨大的垂直磁场中。一种新的拓扑状态是拓扑绝缘体。像普通的绝缘体，例如橡胶，拓扑绝缘体不导电通过材料的内部。与普通绝缘体不同，拓扑绝缘体能够通过形成一种新的物质状态在其边缘或边界上导电。在已知的拓扑绝缘体中，有由元素铋和硒以及铋和碲组成的化合物。PI旨在研究物质拓扑状态中电子之间的强相互作用所产生的电子相关运动的影响。目前对拓扑绝缘体的理解在很大程度上忽略了相关性。PI旨在从几个互补的方面系统地表征相互作用的拓扑状态。相关性可能导致发现具有可用于设备应用的特性的物质的新状态。PI将研究这些状态的性质和量子力学结构。PI将提出新的拓扑状态的实验可观察特征，这些特征定性地来自于熟悉的物质状态。建议的研究将与研究生和本科生的教育相结合。PI将持续努力，通过讲座、课程和研究项目向本科生介绍拟议的研究。PI一直积极组织教程和研讨会，交流科学，使社区的初级和高级成员受益，向更广泛的受众介绍物质拓扑状态的研究成果。PI将准备有关拓扑物理的公开讲座，以传播该项目的研究成果，并吸引物理界以外对该主题的更广泛兴趣。