CAREER: Theoretical Investigation of Interacting Topological States of Matter

该职业奖支持理论研究和教育，以系统地研究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态有了系统的认识。然而，人们对物质的相互作用拓扑态的理解要少得多，并且预计会出现量子数分数化等新的物理现象，正如从分数量子霍尔态中所学到的那样。PI计划通过三种方法的组合来系统地表征不同维度和对称类中物质的相互作用拓扑状态：i）多体基态波函数的构建和表征。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，并构造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。拓扑场论通过拓扑态的可观测物理性质来描述拓扑态。PI的目标是发展新的拓扑场理论的拓扑状态，特别是拓扑超导体。（3）拓扑态的量子纠缠性质及其与系统动力学性质的关系。PI将研究拓扑态的纠缠谱，并开发量子纠缠特性的新特性。拟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独特的研究经验，包括理论凝聚态物理学的扎实训练和许多相关领域的广泛视野。PI将继续努力，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有关物质拓扑状态的研究成果。PI计划准备拓扑物理学的公开讲座，以传播本项目的研究成果，并吸引物理学界以外对该学科更广泛的兴趣。非技术性总结该职业奖支持理论研究和教育，以系统地研究涉及电子相互强烈作用的物质拓扑状态。第一个被发现的物质拓扑状态是量子霍尔效应，这种效应产生于被困在二维薄片中的电子，这些薄片暴露在一个大的垂直磁场中。 一种新的拓扑状态是拓扑绝缘体。像普通的绝缘体一样，例如橡胶，拓扑绝缘体不会通过材料的内部导电。与普通绝缘体不同，拓扑绝缘体能够通过形成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，有铋和硒、铋和碲的化合物。PI的目的是研究电子的相关运动的影响，这些运动是由物质拓扑状态中电子之间的强相互作用引起的。 目前对拓扑绝缘体的理解在很大程度上忽略了相关性。PI的目的是从几个互补的方面系统地描述相互作用的拓扑状态。相关性可以导致发现具有可以用于设备应用的特性的新的物质状态。PI将研究这些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的签名，定性地从熟悉的良好理解的物质状态。拟议的研究将与研究生和本科生的教育相结合。PI将继续努力，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，传播科学，使社区的初级和高级成员受益，向更广泛的受众介绍关于物质拓扑状态的研究成果。PI将准备关于拓扑物理学的公开讲座，以传播该项目的研究成果，并吸引物理学界以外对该主题的更广泛兴趣。

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.