Order, Topology and Transport in Quantum Matter

该奖项支持量子凝聚态物质的理论研究和教育。它旨在加深我们对许多身体系统中出现的新型物质量子态的理解，并确定固体和超冷量子气体中的实验特征和实现。虽然凝聚态物质的朗道范式解释了传统金属和对称破缺态，但这里的重点主要是在这个框架之外的相。例如，拓扑绝缘体和Weyl半金属是允许用非相互作用粒子来描述的相，但它们具有某些特征拓扑性质。外界扰动下电荷、能量和动量的输运有望揭示这些相的基本性质。这些以及与常规顺序的相互作用，特别是拓扑缺陷如漩涡和畴壁，将在本项目的第一部分进行研究。该项目的第二部分涉及强相关拓扑阶段。有希望实现它们的实验制度，如受挫晶格的平坦带和受挫量子磁体，将被研究。对分数量子霍尔态的类似物进行了理论研究，并将其推广到三维空间。精确定位这些状态特征的微妙相关性需要新的探针，特别是那些可以测量非局部属性的探针。提出和评价这些方法将构成该项目的第三个重点领域。该奖项还支持在现代理论凝聚态物理前沿的研究生和博士后研究助理的教育。PI将开发一门新的研究生水平课程，该课程将跨越传统学科，并整合上述研究的方法和结果。研究结果还将通过公开讲座和在公共网站上发布的非技术摘要的方式传播。从技术角度来看，本项目研究的物质量子态的新特性可能会发现具有有用功能和未来应用的新材料。该奖项支持凝聚态系统新状态的理论研究和教育。虽然量子力学定律支配着物质的微观组成部分，但在宏观尺度上观察到的性质往往是经典的；铁基磁铁的磁化就是一个众所周知的例子。然而，最近，人们的注意力已经集中在本质上是量子力学的物质状态上，即使在宏观尺度上，如“量子霍尔态”和“量子自旋液体”，它们正在积极地在磁性材料中寻找。这些新相的一个关键特征是长距离纠缠，这是量子力学行为固有的独特特征。在这个项目中，PI和他的团队将寻求加深我们对这种物质状态的理解，以确定有希望实现它们的领域，并提出实验测试，以表明它们的存在。希望我们在理解上的这些进步将最终导致对这些新状态的更好控制。该奖项还支持在现代理论凝聚态物理前沿的研究生和博士后研究助理的教育。PI将开发一门新的研究生水平课程，该课程将跨越传统学科，并整合上述研究的方法和结果。研究结果还将通过公开讲座和在公共网站上发布的非技术摘要的方式传播。从技术角度来看，本项目研究的物质量子态的新特性可能会发现具有有用功能和未来应用的新材料。

Technical SummaryThis award supports theoretical research and education on quantum condensed matter. It seeks to deepen our understanding of novel quantum states of matter that emerge in many body systems, and to identify experimental signatures and realizations in solids and ultracold quantum gases. While the Landau paradigm of condensed matter accounts for conventional metals and broken symmetry states, here the focus is largely on phases that lie beyond this framework. For example, topological insulators and Weyl semi-metals are phases that admit a description in terms of non-interacting particles, but they possess certain characteristic topological properties. Transport of charge, energy and momentum in the presence of external perturbations are expected to reveal fundamental properties of such phases. These and the interplay with conventional orders, in particular topological defects such as vortices and domain walls, are proposed for study in the first part of this project. The second part of this project addresses strongly correlated topological phases. Promising experimental regimes to realize them, such as flat bands of frustrated lattices and frustrated quantum magnets, will be investigated. Theoretical studies on analogues of fractional quantum Hall states, as well as generalizations to three dimensions are also proposed. Pinpointing the subtle correlations that characterize such states requires new probes, in particular those that can measure non-local properties. Proposing and evaluating such approaches will form the third focus area of this project.This award also supports the education of a graduate student and a postdoctoral research associate at the frontiers of modern theoretical condensed matter physics. The PI will develop a new graduate-level course that cuts across traditional disciplines and integrates the methods and results from the research above. The results will also be disseminated via public lectures and non-technical summaries posted on a public website. From a technological perspective, the novel properties of the quantum states of matter to be investigated in this project can potentially lead to discovery of new materials with useful functionalities and future applications.NonTechnical SummaryThis award supports theoretical research and education on novel states of condensed matter systems. Although quantum mechanical laws govern the microscopic building blocks of matter, the properties observed on a macroscopic scale are often classical; the magnetization of an iron-based magnet being one well-known example. More recently, however, attention has been focused on states of matter which are intrinsically quantum mechanical even at the macroscopic scale, such as "quantum Hall states" as well as "quantum spin liquids" which are actively being sought for in magnetic materials. A key feature of these novel phases is a long range entanglement that is a unique feature intrinsic to quantum mechanical behavior. In this project, the PI and his group will seek to deepen our understanding of such states of matter in order to determine promising arenas for their realization and to propose experimental tests that would signal their presence. It is hoped that these advances in our understanding will eventually lead to a better control over these novel states. This award also supports the education of a graduate student and a postdoctoral research associate at the frontiers of modern theoretical condensed matter physics. The PI will develop a new graduate-level course that cuts across traditional disciplines and integrates the methods and results from the research above. The results will also be disseminated via public lectures and non-technical summaries posted on a public website. From a technological perspective, the novel properties of the quantum states of matter to be investigated in this project can potentially lead to discovery of new materials with useful functionalities and future applications.