CAREER: Quantum Critical Points around Topological Phases

该职业奖支持围绕拓扑秩序的非常规量子临界点研究的理论研究和教育。这些量子临界点超出了经典的朗道-金兹堡范式，它们携带着关于拓扑相本质的重要的、实验可测试的信息。特别是，PI将追求以下方向：(1)了解强相关拓扑态的实验候选，例如受挫自旋为1/2的量子磁体。PI将通过研究这些材料在磁场，压力和其他外部场下的相图来确定这些材料中观察到的奇异态的性质。(2)研究由非平凡量子数拓扑缺陷驱动的量子临界点。在拓扑状态中，如分数拓扑绝缘体，拓扑缺陷通常携带拓扑保护量子数，如电荷、自旋和任意子统计。PI将发展这种拓扑缺陷的多体理论，并理解由这些缺陷驱动的量子临界点的普适类和量子纠缠。(3)探索强相互作用狄拉克费米子的非常规相和量子临界点。狄拉克费米子与许多拓扑态有关，如拓扑带绝缘子。PI将探索由于狄拉克费米子的强相互作用和拓扑之间的相互作用而产生的新物理。例如，PI将研究具有强自旋轨道耦合和相互作用的5d过渡金属氧化物。该奖项还支持教育活动。这包括开发新的课程，强调凝聚态理论的新技术。PI将为学生组织小组会议和研讨会，学生不仅可以拓宽他们的科学学科，还可以锻炼他们的演讲和沟通技巧。将开发一个互动式在线论坛，以激发学生之间的讨论并评估教育的有效性。相关的外展活动包括与教师研究经验项目和加州少数民族参与联盟项目的合作，该项目将为中学教师和弱势学生提供科学研究的资源和机会。该职业奖支持理论研究和教育计划，以研究材料中电子所表现出的被称为拓扑状态的物质的新状态。拓扑状态的一个例子是拓扑绝缘体。像普通的绝缘体，例如橡胶，拓扑绝缘体不导电通过材料的内部。与普通绝缘体不同，拓扑绝缘体能够通过形成一种新的物质状态在其边缘或边界上导电。在已知的拓扑绝缘体中，有由元素铋和硒以及铋和碲组成的化合物。PI旨在通过研究物质状态之间的转换而不是涉及拓扑状态来推进对物质拓扑状态的理解。拓扑状态从根本上不同于我们所熟悉的物质状态，比如绝缘体和金属状态。涉及这些状态的相变不符合相变的标准理论。PI的目标是利用发生在绝对零度温度下的状态之间的转换，称为量子相变，以确定拓扑状态的性质，并将表现出拓扑状态候选电子状态的材料实验和模型系统的计算机模拟联系起来。这项研究直接关系到材料的挫折磁铁。在这些材料中，由于原子的几何排列，基本微观磁性单位（电子自旋）之间的相互作用不能得到满足。PI的目的是通过比较实验确定的相图与PI的理论预测来了解这些非常规状态的本质。该奖项支持教育活动，目的是在学生学习基础物理的同时提高研究的创造力和创新能力。将开设以现代凝聚态理论为重点的新课程。将设计一个新的在线论坛来激发讨论，并评估教学效果。PI将开展外联活动，为中学教师和代表性不足的学生提供研究机会。

TECHNICAL SUMMARYThis CAREER award supports theoretical research and education focused on the study of unconventional quantum critical points around topological order. These quantum critical points are beyond the classic Landau-Ginzburg paradigm, and they carry important and experimentally testable information on the nature of the topological phases. In particular, the PI will pursue the following directions: (1) Understanding the experimental candidates of strongly correlated topological states, for example frustrated spin-1/2 quantum magnets. The PI will identify the nature of the exotic states observed in these materials by studying the phase diagram of these materials under magnetic field, pressure, and other external fields. (2) Investigating the quantum critical points driven by topological defects with nontrivial quantum numbers. In topological states such as a fractional topological insulator, a topological defect usually carries topologically protected quantum numbers such as charge, spin, and anyon statistics. The PI will develop a many-body theory of such topological defects, and understand the universality class and quantum entanglement at the quantum critical points driven by these defects.(3) Exploring unconventional phases and quantum critical points of strongly interacting Dirac fermions. Dirac fermions are related to many topological states such as topological band insulators. The PI will explore the novel physics due to the interplay between the strong interaction and topology of Dirac fermions. For example, the PI will investigate the 5d transition metal oxides with both strong spin-orbit coupling and interaction. This award also supports educational activities. These include developing new courses with emphasis on new techniques in condensed matter theory. The PI will organize group meetings and seminars for students, where the students will not only broaden their scientific disciplines, but also practice their presentation and communication skills. An interactive online Forum will be developed in order to stimulate discussions between students and to evaluate the effectiveness of education. The associated outreach activities include partnerships with a Research Experience for Teachers program, and California Alliance for Minority Participation program which will provide resources and opportunities in scientific research to secondary school teachers and under-represented students. NON-TECHNICAL SUMMARYThis CAREER award supports theoretical research and education programs to study new states of matter called topological states that are exhibited by electrons in materials. An example of a topological state is a topological insulator. Like ordinary insulators, for example rubber, topological insulators do not conduct electricity though the interior of the material. Unlike ordinary insulators, topological insulators are able to conduct electricity on their edges or boundaries through the formation of a new state of matter. Among the known topological insulators are compounds made of the elements bismuth and selenium, and bismuth and tellurium. The PI aims to advance understanding of topological states of matter by investigating the transformations between states of matter than involve topological states. Topological states fundamentally differ from more familiar states of matter like insulators and metallic states. Transformations involving these states do not fit the standard theory of phase transitions. The PI aims to use transformations among states that occur at the absolute zero of temperature called quantum phase transitions to determine the properties of topological states and connect to experiments on materials that exhibit electronic states that are candidates for topological states and to computer simulations on model systems. This research has immediate relevance to materials that are frustrated magnets. In these materials the interactions between fundamental microscopic units of magnetism, the electron spin, cannot be satisfied because of the geometric arrangement of atoms. The PI aims to understand the nature of these unconventional states by comparing the experimentally determined diagram of phases with the PI's theoretical predictions. This award supports educational activities with the goal to improve creativity and innovation in research while students learn basic physics. New courses with emphasis on modern condensed matter theory will be developed. A new online forum will be designed to stimulate discussion, and evaluate teaching effectiveness. The PI will carry out outreach activities that provide research opportunities to secondary school teachers and under-represented students.