CAREER: Topology and Symmetry in Physics Beyond the Landau Paradigm

非技术性总结该职业奖支持理论研究和教育，以研究材料中电子的量子力学状态以及它们之间的转换，这些转换需要新的理论概念来描述。 实验发现和理论进展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从一种物质状态到另一种物质状态的转换的标准概念框架，并用于描述材料中相互强烈相互作用的电子状态。 为了促进对这些和其他预测的新物质状态及其之间的转换的理解，PI将专注于三项主要活动：（一）开发理论和计算工具，以了解当物理条件改变时会发生什么，以驱动相位之间的转换，由于电子的集体行为，这些相位似乎是由具有基本电荷的一小部分的粒子组成的电子电荷;（2）开发理论模型，以促进对一种全新的材料系统的理解，在这种材料系统中，三维材料具有仅存在于边界处的有趣的电子状态;（3）提出新的实验，可以检测预测在特殊工程材料中发生的分数粒子。本研究为研究生提供了模拟训练。 PI将通过旨在激发中学学生对科学的兴趣的外展活动，帮助传达材料研究的兴奋。 PI将与当地高中教师和学生合作，开发基于网络的学习工具，让学生探索日常生活中熟悉的许多技术背后的材料科学。 其目的是让学生以自己的节奏，以直观而非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，例如超导性，以及带有电子电荷的一小部分的粒子的出现。技术总结该职业奖支持理论研究和教育活动，重点关注理解物质相以外的物质相朗道范式;这些系统的物理学既不能用费米液体理论来完全理解，也不能通过考虑可能的破坏有序状态来完全理解。 具体来说，该项目侧重于两种类型的现象没有捕捉到这些框架：拓扑秩序在1D和2D，和对称性保护强相互作用的3D系统。 该研究有三个主要组成部分：1）。提高对二维拓扑有序系统中的相图和相变的理解。PI计划建立在现有的数值和理论工具的基础上，以更好地理解2D中不同拓扑顺序的相之间的临界性。 这些转变是有趣的和具有挑战性的研究，因为临界自由度的拓扑特征意味着没有局部序参量存在，从根本上说，新的工具是必要的。 将寻求发生这种转变的实验现实系统。为了促进对3D中强相互作用的量子保护相的理解，PI将开发理论模型并确定相关的场论。 特别关注的是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上。 PI的目的是量化新的实验探针，可以帮助识别激发与非阿贝尔统计。 最近在实验室中以新的方式实现这些的建议提出了理解这些系统的可行和可靠的检测技术的挑战。 这项研究将建立在这些系统的有限频率响应如何表征其拓扑性质的现有知识的基础上，这项研究为研究生提供了模拟训练。 PI将通过旨在激发中学学生对科学的兴趣的外展活动，帮助传达材料研究的兴奋。 PI将与当地高中教师和学生合作，开发基于网络的学习工具，让学生探索日常生活中熟悉的许多技术背后的材料科学。 其目的是让学生以自己的节奏，以直观而非数学的方式探索许多相互作用的量子粒子系统的一些更令人惊讶的特性，例如超导性，以及带有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.