RUI: Numerical Studies of Topological Ordered Phases in Realistic Models

RUI：现实模型中拓扑有序相的数值研究

• 批准号: 1508290
• 负责人: Michael Peterson
• 金额: $ 19.83万
• 依托单位: California State University-Long Beach Foundation
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2015
• 资助国家: 美国
• 起止时间: 2015-09-15 至 2019-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1508290&HistoricalAwards=false
• 关键词: RUI; Numerical; Studies; Topological; Ordered

NONTECHNICAL SUMMARY This award supports theoretical and computational research and education on new electronic states of matter in two-dimensions. Electrons can be confined to two-dimensions within specially made semiconductor devices and in some two-dimensional materials. When a high magnetic field is applied to that electron system at very low temperatures, the fractional quantum Hall effect emerges. In the magnetic field the electrons interact strongly and forgo their individuality: the electron system collectively behaves as if it is comprised of other particles, called anyons, with exotic properties. For example, anyons can appear carrying only a fraction, e.g. one-third of the electron charge. This strange behavior, which fundamentally relies on the cooperation of all the electrons in the system, is a hallmark of a topologically ordered state of matter; their study is currently at the forefront of physics, materials science, and mathematics. A particular type of anyon, called a non-Abelian anyon, has been proposed as a building block for the construction of a quantum computer, a type of computer that is particularly efficient for problems ordinary computers would take an unacceptably long time to solve. Using computer simulations and new theoretical techniques, the PI will address fundamental questions about the experimental realization of non-Abelian anyons in topologically ordered phases. The educational elements will involve modern and exciting research opportunities for the ethnically, culturally, and economically diverse graduate and undergraduate students at the California State University Long Beach (CSULB). The award will aim to recruit more high school students from the greater Los Angeles area to attend CSULB and major in physics or other STEM fields, educate high school teachers about the many interesting facets of condensed matter, and recruit and retain physics majors already enrolled at CSULB. TECHNICAL SUMMARY This award supports theoretical and computational research and education focusing on numerical studies of topologically ordered phases emerging in realistic condensed matter physics models. The research will concentrate on two canonical physical systems: the fractional quantum Hall effect (FQHE), and quantum spin models. Using computationally intensive numerical techniques and advanced theoretical concepts on realistic models, the PI will address central and important questions about the realization of non-Abelian anyons in the FQHE in semiconductor heterostructures and graphene, and the possibility of topologically ordered states in low-dimensional quantum spin models. The PI will resolve questions and stimulate future research in the search for topologically ordered states in realistic systems, contributing to a foundation of knowledge from which to construct a quantum computer. The research questions being addressed in this project are: Do non-Abelian anyonic quasiparticle excitations exist in the FQHE under realistic conditions? Are there topologically ordered phases in realistic low-dimensional quantum spin models, and if so, what is their nature? The educational elements will involve modern and exciting research opportunities for the ethnically, culturally, and economically diverse graduate and undergraduate students at the California State University Long Beach (CSULB). The award will aim to recruit more high school students from the greater Los Angeles area to attend CSULB and major in physics or other STEM fields, educate high school teachers about the many interesting facets of condensed matter, and recruit and retain physics majors already enrolled at CSULB.

非技术摘要 该奖项支持二维物质新电子态的理论和计算研究及教育。电子可以被限制在特制半导体器件和某些二维材料中的二维范围内。当在非常低的温度下向该电子系统施加高磁场时，就会出现分数量子霍尔效应。在磁场中，电子强烈相互作用并放弃其个体性：电子系统的集体行为就好像它是由其他粒子（称为任意子）组成，具有奇异的特性。例如，任意子可能只携带一小部分，例如电子电荷的三分之一。这种奇怪的行为从根本上依赖于系统中所有电子的合作，是拓扑有序物质状态的标志。他们的研究目前处于物理学、材料科学和数学的前沿。一种特殊类型的任意子，称为非阿贝尔任意子，已被提议作为构建量子计算机的构建块，这种计算机对于解决普通计算机需要很长时间才能解决的问题特别有效。使用计算机模拟和新的理论技术，PI 将解决有关拓扑有序相中非阿贝尔任意子实验实现的基本问题。教育元素将包括为加州州立大学长滩分校 (CSULB) 的种族、文化和经济多元化的研究生和本科生提供现代且令人兴奋的研究机会。该奖项旨在招募更多来自大洛杉矶地区的高中生来 CSULB 学习物理学或其他 STEM 领域的专业，教育高中教师了解凝聚态物质的许多有趣方面，并招募和留住已在 CSULB 就读的物理专业学生。技术摘要 该奖项支持理论和计算研究及教育，重点关注现实凝聚态物理模型中出现的拓扑有序相的数值研究。该研究将集中在两个典型的物理系统：分数量子霍尔效应（FQHE）和量子自旋模型。利用计算密集型数值技术和现实模型上的先进理论概念，PI 将解决有关在半导体异质结构和石墨烯中实现 FQHE 中非阿贝尔任意子的核心和重要问题，以及低维量子自旋模型中拓扑有序态的可能性。该 PI 将解决问题并促进未来在现实系统中寻找拓扑有序状态的研究，为构建量子计算机奠定知识基础。该项目要解决的研究问题是：在现实条件下，FQHE 中是否存在非阿贝尔任意子准粒子激发？现实的低维量子自旋模型中是否存在拓扑有序相？如果存在，它们的本质是什么？教育元素将包括为加州州立大学长滩分校 (CSULB) 的种族、文化和经济多元化的研究生和本科生提供现代且令人兴奋的研究机会。该奖项旨在招募更多来自大洛杉矶地区的高中生来 CSULB 学习物理学或其他 STEM 领域的专业，教育高中教师了解凝聚态物质的许多有趣方面，并招募和留住已在 CSULB 就读的物理专业学生。