RUI: Numerical Studies of Topological Ordered Phases in Realistic Models

该奖项支持二维物质新电子态的理论和计算研究和教育。在特殊制造的半导体器件和一些二维材料中，电子可以被限制在二维空间。当在极低温度下对电子系统施加高磁场时，分数量子霍尔效应就出现了。在磁场中，电子相互作用强烈，并放弃了它们的个性：电子系统的整体行为就好像是由其他具有奇异性质的粒子组成的，这些粒子被称为任意子。例如，任何子都可能只携带一小部分，例如三分之一的电子电荷。这种奇怪的行为从根本上依赖于系统中所有电子的合作，是物质拓扑有序状态的标志；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，被称为非阿贝尔任意子，已经被提议作为构建量子计算机的基石，这种类型的计算机特别有效，可以解决普通计算机需要很长时间才能解决的问题。利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。教育元素将涉及现代和令人兴奋的研究机会，为种族，文化和经济多样化的研究生和本科生在加州州立大学长滩（CSULB）。该奖项旨在招募更多来自大洛杉矶地区的高中生参加CSULB并主修物理或其他STEM领域，向高中教师介绍凝聚态物质的许多有趣方面，并招募和留住已经在CSULB注册的物理专业学生。该奖项支持理论和计算研究和教育，重点是在现实凝聚态物理模型中出现的拓扑有序相的数值研究。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。利用计算密集型的数值技术和现实模型上的先进理论概念，PI将解决有关半导体异质结构和石墨烯中FQHE中非阿贝尔任意子的实现的核心和重要问题，以及低维量子自旋模型中拓扑有序态的可能性。PI将解决问题，并刺激在现实系统中寻找拓扑有序状态的未来研究，为构建量子计算机奠定知识基础。本课题主要研究的问题是：在现实条件下，在FQHE中是否存在非阿贝尔任意子准粒子激发？在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，它们的性质是什么？教育元素将涉及现代和令人兴奋的研究机会，为种族，文化和经济多样化的研究生和本科生在加州州立大学长滩（CSULB）。该奖项旨在招募更多来自大洛杉矶地区的高中生参加CSULB并主修物理或其他STEM领域，向高中教师介绍凝聚态物质的许多有趣方面，并招募和留住已经在CSULB注册的物理专业学生。

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.