CAREER: Topology and Symmetry in Physics Beyond the Landau Paradigm

该职业奖支持理论研究和教育，以调查材料中电子的量子力学状态以及它们之间需要新的理论概念来描述的转换。实验发现和理论进步揭示了物质的新特性和电子状态，这些特性和电子状态超出了用于描述物质从一种状态转变为另一种状态的标准概念框架，并用于描述材料中相互作用强烈的电子状态。为了促进对这些和其他预测的新物质状态及其之间转换的理解，PI将专注于三个主要活动：(1)开发理论和计算工具，以了解当物理条件发生变化时发生的情况，以驱动相之间的转换，由于电子的集体行为似乎是由带有基本电子电荷的一小部分的粒子组成；(2)发展理论模型，以促进对一种全新材料系统的理解，在这种系统中，三维材料拥有仅存在于边界的有趣的电子状态；(3)提出新的实验，可以检测预测在特殊工程材料中出现的分数粒子。本研究为研究生提供了模拟训练。PI将通过旨在激发中学生对科学的兴趣的外展活动，帮助传达材料研究的兴奋。通过与当地高中教师和学生的合作，PI将开发基于网络的学习工具，使学生能够探索日常生活中熟悉的许多技术背后的材料科学。目的是让学生按照自己的节奏，以直观的方式，而不是数学的方式，探索许多相互作用的量子粒子系统的一些更惊人的特性，比如超导性，以及带有一小部分电子电荷的粒子的出现。该职业奖支持理论研究和教育活动，重点是理解朗道范式之外的物质阶段；这些系统的物理学既不能用费米液体理论完全理解，也不能考虑可能的对称破缺有序态。具体来说，该项目侧重于两种未被这些框架捕获的现象：1D和2D的拓扑顺序，以及强相互作用3D系统中的对称保护。这项研究有三个主要组成部分：1)促进对二维拓扑有序系统的相图和相变的理解。PI计划以现有的数值和理论工具为基础，更好地理解二维中不同拓扑顺序相之间的临界性。这些转换的研究既有趣又具有挑战性，因为临界自由度的拓扑特征意味着不存在局部顺序参数，并且从根本上需要新的工具。我们将寻求在实验上能够实现这种转变的系统。为了促进对三维强相互作用对称保护相的理解，PI将开发理论模型并确定相关的场理论。特别关注这些强相互作用系统中缺陷和表面状态的拓扑特征，建立在成功应用于非相互作用系统的方法之上。PI的目标是量化新的实验探针，这些探针可以帮助识别非阿贝尔统计的激发。最近在实验室中以新方式实现这些的建议提出了理解这些系统可行和可靠的检测技术的挑战。这项研究将建立在现有知识的基础上，即这些系统中的有限频率响应如何表征其拓扑性质。本研究为研究生提供了模拟训练。PI将通过旨在激发中学生对科学的兴趣的外展活动，帮助传达材料研究的兴奋。通过与当地高中教师和学生的合作，PI将开发基于网络的学习工具，使学生能够探索日常生活中熟悉的许多技术背后的材料科学。目的是让学生按照自己的节奏，以直观的方式，而不是数学的方式，探索许多相互作用的量子粒子系统的一些更惊人的特性，比如超导性，以及带有一小部分电子电荷的粒子的出现。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education to investigate quantum mechanical states of electrons in materials and transformations among them that require new theoretical concepts for their description. Experimental discoveries and theoretical advances reveal novel properties and electronic states of matter that lie outside the standard conceptual framework used to describe the transformation from one state of matter into another, and used to describe the state of electrons that interact strongly with each other in materials. To advance understanding of these and other predicted new states of matter and the transformations among them, the PI will focus on three major activities: (1) developing theoretical and computational tools to understand what happens as physical conditions are changed to drive transformations between phases that owing to the collective behavior of the electrons appear to be made of particles with a charge that is a fraction of a fundamental electron charge; (2) developing theoretical models to advance understanding of a fundamentally new kind of material system, in which a 3 dimensional material hosts interesting electric states that exist only at the boundaries; and(3) proposing new experiments that can detect fractional particles that are predicted to occur in specially engineered materials. The research provides simulating training for graduate students. The PI will help convey the excitement of materials research through outreach activities aimed at inspiring interest in the science among students at the secondary school level. In collaboration with local high-school teachers, as well as students, the PI will develop web-based learning tools allowing students to explore the materials science underlying many of the technologies familiar from daily life. The objective is to allow students to explore at their own pace and in an intuitive, rather than mathematical, way some of the more astonishing properties of systems of many interacting quantum particles, such as superconductivity, and emergence of particles with charges that are a fraction of an electron charge.TECHNICAL SUMMARYThis CAREER award supports theoretical research and educational activities focused on understanding phases of matter beyond the Landau paradigm; systems whose physics cannot be fully understood either by Fermi liquid theory, or by considering possible symmetry-breaking ordered states. Specifically, this project focuses on two types of phenomena not captured by either of these frameworks: topological order in 1D and 2D, and symmetry protection in strongly interacting 3D systems. The research has three main components: 1.) To advance understanding of the phase diagrams and phase transitions in 2D topologically ordered systems. The PI plans to build on existing numerical and theoretical tools to better understand criticality between phases of different topological order in 2D. These transitions are interesting and challenging to study because the topological character of the critical degrees of freedom implies that no local order parameter exists, and fundamentally new tools are needed. Experimentally realistic systems where such transitions occur will be sought.2.) To advance understanding of strongly interacting symmetry-protected phases in 3D, the PI will develop theoretical models and identify the relevant field theories. The particular focus will be on the topological character of defects and surface states in these strongly interacting systems, building on methods applied successfully to non-interacting systems.3.) The PI aims to quantify new experimental probes that can help identify excitations with non-abelian statistics. Recent proposals for realizing these in new ways in the laboratory have raised the challenge of understanding feasible and reliable detection techniques for these systems. The research will build on existing knowledge of how finite-frequency responses in these systems characterize their topological nature.The research provides simulating training for graduate students. The PI will help convey the excitement of materials research through outreach activities aimed at inspiring interest in the science among students at the secondary school level. In collaboration with local high-school teachers, as well as students, the PI will develop web-based learning tools allowing students to explore the materials science underlying many of the technologies familiar from daily life. The objective is to allow students to explore at their own pace and in an intuitive, rather than mathematical, way some of the more astonishing properties of systems of many interacting quantum particles, such as superconductivity, and emergence of particles with charges that are a fraction of an electron charge.