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.

非技术摘要这一职业奖支持对电子在材料中的自我组织的基本理论研究，这些研究是拓扑顺序特征的物质量子机械阶段。实验无法通过探测材料的小部分来区分此类阶段，而必须执行实际上探测样品整个范围的测量。这表明拓扑阶段可能是用于存储和操纵量子力学信息的有效工具。与熟悉的信息存储技术相反，信息将在拓扑阶段进行全球编码，并受到保护，免受物质缺陷和其他外部干扰来源的有害影响，这些效果通常仅限于小区域。实施这一有趣的想法来构建拓扑量子计算机是一个主要的技术挑战，而了解物质这些异常阶段的行为是一个基本问题。该项目从两个方向探讨了这些目标。首先是从其结晶宿主材料的对称性的角度从对拓扑阶段进行系统的理解。这将使新的拓扑阶段的识别和分类，包括金属和半导体之间的“半金属”中间体，这些中间体可能为新的量子设备提供平台。第二个方向是了解简单的量子计算机的行为：由与周围环境隔离的量子力学定律管辖的许多交互计算机位的系统。 PI将检查此类系统是否可以避免发展为热平衡状态，从而可以消除其量子信息含量。 PI旨在开发技术来探测这种平衡时产生的异常阶段。从基本意义上讲，这些量子状态类似于“眼镜”，似乎代表了一种从根本上由量子力学支配的新型系统，具有新的和令人惊讶的行为和应用。和外展计划。一项努力将使用发人深省的实验来暴露中学生 - 主要是从具有很大社会经济地位的学生比例的学校中汲取的 - 基本科学问题。这将建立在PI机构的现有外展计划中，并通过为其教师提供材料和指导来复制课堂上的此类发现活动，从而超越它们。 PI将在研究生和本科级别开发新课程，并建立一个期刊俱乐部，以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，他们将受到积极指导，并有机会参加国家和国际科学合作或会议。 PI还将找到一所每两年一次的暑期学校，为南加州的初学者做好准备，以供凝结物理学的研究职业。该学校将通过鼓励非传统和少数族裔学生参与加利福尼亚州立大学系统的参与来促进多样性。技术摘要该职业奖支持理论研究对凝结物质系统的理论研究，在这些系统中，组成粒子之间的相互作用导致物质的拓扑阶段。这样的阶段可能与量子计算机建立耐腐蚀性的拓扑量子量相关。研究活动的第一个推力将研究结晶对称性如何描述物质的可能阶段，并在PI和合作者的先前工作基础上证明了“非 - 非 - ”的作用。符号的对称性。 PI概括了这些想法，将研究旋转轨道和互相互作用导致新阶段的系统。 PI还将使用简单的确切可解决的模型来检查这种对称性如何导致Landau-Forbidding相变。武装这些结果，P.I。将分析相互作用的拓扑结晶绝缘子的分类。最后，将研究由于结晶对称性或能量带之间的意外变性而出现的半金属的新型传输特性，并重点是它们与量子异常的联系。第二个广泛的方向研究了拓扑阶段对杂质的反应。将解决三个主要问题：（i）开发新的动力探针，能够辨别相互作用对无序的孤立拓扑系统的微妙影响； （ii）分析非亚伯人的无序链的行为，以研究其实现新型多体局部阶段的潜力； （iii）无序量子大厅系统中颗粒相的可能性，类似于肮脏的超导体中的类似相，这将代表异常的拓扑问题。还将实施一项全面的教育计划，该计划将这些研究目标纳入针对K-12学生，本科和研究生研究和指导，初级研究人员的课程和专业发展的外展活动。该项目还将建立两年一的暑期学校，以准备在南加州的初学者准备重新搜索物理学的重新搜索职业。