CAREER: Topology, Symmetry and Disorder in Strongly Correlated Systems

职业：强相关系统中的拓扑、对称和无序

• 批准号: 1455366
• 负责人: Alexander Chernyshev
• 金额: $ 50.5万
• 依托单位: University of California-Irvine
• 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: 2015-07-01 至 2019-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1455366&HistoricalAwards=false
• 关键词: CAREER; Topology; Symmetry; Disorder; Strongly

NONTECHNICAL SUMMARYThis CAREER award supports basic theoretical research on the self-organization of electrons in materials that are quantum mechanical phases of matter characterized by topological order. Experiments cannot distinguish among such phases by probing small pieces of the material, but instead must perform measurements that in effect probe the entire extent of a sample. This suggests that topological phases may be potent tools for storing and manipulating quantum-mechanical information. In contrast to familiar information storage technologies, information would be encoded globally in a topological phase and would be protected against the detrimental effects of material imperfections and other extrinsic sources of interference, that are generally confined to small regions. Implementing this intriguing idea to build a topological quantum computer is a major technical challenge, while understanding the behavior of these unusual phases of matter is a fundamental problem.This project approaches these goals from two directions. The first is to develop a systematic understanding of topological phases from the perspective of the symmetry of their crystalline host materials. This will enable the identification and classification of new topological phases, including 'semi-metals' intermediate between metals and semiconductors that may provide platforms for new quantum devices. The second direction is to understand the behavior of a simple quantum computer: a system of many interacting computer bits governed by the laws of quantum mechanics isolated from their surroundings. The PI will examine whether such systems can avoid evolving into a state of thermal equilibrium which could wash out their quantum information content. The PI aims to develop techniques to probe the unusual phases that result when such an equilibrium is evaded. In a fundamental sense, these quantum states resemble 'glasses' and appear to represent a fundamentally new type of system governed by quantum mechanics, with the potential for new and surprising behaviors and applications.Alongside these research goals, the PI will implement a comprehensive education and outreach plan. One effort will use thought-provoking experiments to expose middle school students - drawn predominantly from schools with a large proportion of students of low socio-economic status - to basic scientific questions. This will build in to existing outreach programs at the PI's institution, and go beyond them by providing materials and guidance for their teachers to duplicate such discovery activities in the classroom. The PI will develop new courses at the graduate and undergraduate levels and establish a journal club to acquaint graduate students with research literature. The project includes funding for graduate and undergraduate students, who will be actively mentored and given the opportunity to participate in both national and international scientific collaborations or conferences. The PI will also found a biennial summer school to prepare beginning graduate students in Southern California for research careers in condensed matter physics. The school will promote diversity by encouraging participation by nontraditional and minority students in the California State University system.TECHNICAL SUMMARY This CAREER award supports theoretical research into condensed matter systems where interactions among constituent particles lead to topological phases of matter. Such phases are potentially relevant to building decoherence-resistant topological qubits for quantum computers.The first thrust of the research activity will examine how crystalline symmetries delineate possible phases of matter, building on prior work by the PI and collaborators demonstrating the role of 'non-symmorphic' symmetries. Generalizing these ideas, the PI will study systems where spin-orbit and interelectron interactions lead to new phases. The PI will also examine how such symmetries lead to Landau-forbidden phase transitions, using simple exactly solvable models. Armed with these results, the P.I. will analyze the classification of interacting topological crystalline insulators. Finally, the novel transport properties of the semi-metals that emerge as a consequence of crystalline symmetries or accidental degeneracies between energy bands will be studied, with an emphasis on their connection to quantum anomalies. The second broad direction examines the response of topological phases to impurities. Three main problems will be addressed: (i) the development of new dynamical probes capable of discerning subtle effects of interactions on disordered, isolated topological systems; (ii) an analysis of the behavior of disordered chains of non-Abelian anyons to examine their potential for realizing novel many-body localized phases with low entanglement; and (iii) the possibility of granular phases in disordered quantum Hall systems, similar to analogous phases in dirty superconductors, which would represent an unusual form of topological matter.The P.I. will also implement a comprehensive education plan that integrates these research goals into outreach aimed at K-12 students, undergraduate and graduate research and mentoring, curricular and professional development of junior researchers. The project will also establish a biennial summer school to prepare beginning graduate students in Southern California for re-search careers in condensed matter physics.

该职业奖支持材料中电子自组织的基础理论研究，这些材料是具有拓扑顺序特征的物质的量子力学相。实验不能通过探测材料的小块来区分这些阶段，而是必须进行测量，实际上探测样品的整个范围。这表明拓扑相可能是存储和操纵量子力学信息的有力工具。与熟悉的信息存储技术相比，信息将在拓扑阶段进行全局编码，并将受到保护，免受材料缺陷和其他外部干扰源的有害影响，这些干扰源通常局限于小区域。实现这个有趣的想法来构建拓扑量子计算机是一个重大的技术挑战，而理解这些不寻常的物质相的行为是一个基本问题。这个项目从两个方向实现了这些目标。首先是从晶体主体材料的对称性角度对拓扑相进行系统的理解。这将使新的拓扑相的识别和分类成为可能，包括介于金属和半导体之间的“半金属”，这可能为新的量子器件提供平台。第二个方向是理解简单量子计算机的行为：一个由许多相互作用的计算机位组成的系统，这些计算机位受量子力学定律的支配，与周围环境隔离。PI将检查这样的系统是否可以避免进化到热平衡状态，因为热平衡状态可能会冲掉它们的量子信息内容。PI的目标是开发技术来探测当这种平衡被规避时产生的不寻常阶段。从基本意义上讲，这些量子态类似于“玻璃”，似乎代表了一种由量子力学控制的全新类型的系统，具有新的令人惊讶的行为和应用的潜力。除了这些研究目标外，PI还将实施一项全面的教育和推广计划。其中一项努力将使用发人深省的实验，让中学生接触基本的科学问题。这些中学生主要来自那些社会经济地位低的学生占很大比例的学校。这将建立在PI所在机构现有的外展项目中，并在此基础上为教师提供材料和指导，让他们在课堂上重复这种发现活动。PI将在研究生和本科生阶段开设新课程，并建立一个期刊俱乐部，使研究生熟悉研究文献。该项目包括为研究生和本科生提供资金，他们将得到积极的指导，并有机会参加国内和国际科学合作或会议。PI还将成立一个两年一次的暑期学校，为南加州的刚开始从事凝聚态物理研究的研究生做准备。学校将通过鼓励非传统和少数民族学生参与加州州立大学系统来促进多样性。该职业奖支持凝聚态系统的理论研究，在凝聚态系统中，组成粒子之间的相互作用导致物质的拓扑相。这些相位可能与为量子计算机构建抗退相干拓扑量子比特有关。研究活动的第一个重点将是研究晶体对称性如何描述物质的可能相，以PI和合作者先前的工作为基础，证明“非对称”对称性的作用。推广这些想法，PI将研究自旋轨道和电子间相互作用导致新相的系统。PI还将使用简单的精确可解模型来研究这种对称性如何导致朗道禁相转变。有了这些结果，P.I.将分析相互作用拓扑晶体绝缘体的分类。最后，将研究由于晶体对称或能量带之间的偶然简并而出现的半金属的新输运性质，重点是它们与量子异常的联系。第二个大方向研究拓扑相对杂质的响应。将解决三个主要问题：(i)开发新的动态探针，能够识别相互作用对无序孤立拓扑系统的微妙影响；（ii）分析非阿贝尔任意子的无序链的行为，以研究它们实现低纠缠的新型多体局域相的潜力；（iii）无序量子霍尔系统中颗粒相的可能性，类似于脏超导体中的类似相，这将代表一种不寻常的拓扑物质形式。pi还将实施一项全面的教育计划，将这些研究目标整合到针对K-12学生、本科生和研究生的研究和指导、初级研究人员的课程和专业发展中。该项目还将建立一个两年一次的暑期学校，为南加州的刚开始从事凝聚态物理研究的研究生做好准备。