Interplay of Topological Order and Symmetry In and Out of Equilibrium

拓扑序和对称性在平衡状态和非平衡状态下的相互作用

基本信息

批准号：
1939864
负责人：
Lukasz Fidkowski
金额：
$ 33.73万
依托单位：
University of Washington
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-01-01 至 2023-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1939864&HistoricalAwards=false
关键词：
Interplay Topological Order Symmetry Out

项目摘要

NONTECHNICAL SUMMARYThis award supports theoretical research and education on exotic low temperature states of condensed matter systems. Although quantum mechanics describes the behavior of matter at the microscopic level, quantum mechanical effects are typically not visible at the macroscopic scale. In the 1980s a new class of so-called `topologically ordered' states was discovered in studying the quantum Hall effect in which electrons are confined in a plane between two semiconductors and placed in a high magnetic field perpendicular to the plane. The quantum Hall states show quantum effects that are felt at the macroscopic scale. These include the emergence of particle like behavior that carries only a fraction of the electron charge and channels which only allow charge to flow in one direction.To gain a better understanding of what kinds of new states of electrons can be realized in materials and how they can be detected experimentally, the PI and collaborators will combine methods from theoretical condensed matter physics and the field of quantum information theory which is comprised of ideas from information theory, quantum mechanics, mathematics, and computer science. Quantum information theory provides a useful way to think about aspect of computing and information transmission involving the manipulation of quantum mechanical states. This award also supports the education of a graduate student at the frontiers of modern theoretical condensed matter physics. Furthermore, the PI will continue to develop a graduate level course that incorporates new material from quantum information theory in addition to standard condensed matter field theory. In addition, the work may have an additional positive impact in that condensed matter ideas may potentially lead to advances in quantum information and quantum computation.TECHNICAL SUMMARYThis award supports theoretical research and education on the combined effects of symmetry and topology in strongly correlated many-body quantum systems. Such strongly correlated systems can realize zero-temperature phases of matter beyond the standard Ginzburg-Landau-Wilson symmetry breaking paradigm. These can have intrinsic topological order and support fractionalized `anyon' excitations, or they can be symmetry protected.A large portion of this project will be to classify phases of matter which exhibit intrinsic topological order, symmetry-protected features, or both. This will include both equilibrium zero temperature gapped quantum phases and many-body localized (MBL) out of equilibrium systems. Specific areas of focus include: 1) classifying fermionic symmetry protected phases and understanding the strongly correlated topological surface states they can exhibit, 2) extracting universal properties of topological and symmetry protected phases from commuting projector lattice Hamiltonians and understanding the conditions under which such commuting projector Hamiltonians exist, and 3) classifying topological phases in periodically driven (Floquet) MBL quantum systems. The PI will use analytical tools, such as quantum field theory and exactly solvable models, to prove the existence of gapped phases, and will also use mathematical methods, such as topological quantum field theory and algebraic topology, to study and potentially rule out putative patterns of topological order. The PI will develop new quantum-information theoretic tools to address these problems.This project has the potential to develop fundamental understanding of topological order in and out of equilibrium. In particular, the problem of classifying topological order in non-equilibrium MBL systems is not necessarily amenable to the same field theory techniques as is the equilibrium case, but can be usefully addressed with quantum information theory methods. The PI will build on ongoing work with collaborators within the quantum information community to develop such methods, which recent results indicate will be useful for both the physics and quantum information communities.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

非技术摘要这一奖项支持有关凝结物质系统的异国情调低温状态的理论研究和教育。尽管量子力学描述了物质在微观水平上的行为，但量子力学效应通常在宏观尺度上不可见。在1980年代，在研究量子厅效应时发现了一类新的所谓“拓扑排序”状态，在研究量子厅效应中，其中电子被限制在两个半导体之间的平面中，并放置在垂直于平面的高磁场中。量子厅状态显示在宏观尺度上感觉到的量子效应。 These include the emergence of particle like behavior that carries only a fraction of the electron charge and channels which only allow charge to flow in one direction.To gain a better understanding of what kinds of new states of electrons can be realized in materials and how they can be detected experimentally, the PI and collaborators will combine methods from theoretical condensed matter physics and the field of quantum information theory which is comprised of ideas from information theory, quantum mechanics, mathematics, and 计算机科学。量子信息理论提供了一种有用的方法来思考涉及量子机械状态操纵的计算和信息传输方面。该奖项还支持现代理论凝结物理学领域的研究生的教育。此外，PI将继续开发研究生级别的课程，该课程除了标准凝结物质现场理论外，还结合了量子信息理论的新材料。此外，这项工作可能会产生额外的积极影响，因为凝结物的想法可能有可能导致量子信息和量子计算的进步。技术摘要这一奖项支持理论研究和教育对对称性和拓扑在密切相关的多体量子系统中对对称性和拓扑的综合影响。如此强大的相关系统可以实现物质的零温度阶段，超出标准的金兹堡 - 兰道 - 威尔逊对称性破坏范式。这些可以具有内在的拓扑顺序并支持分数化的“ Anyon”激发，也可以受到对称的保护。该项目的很大一部分将是对具有内在拓扑顺序，对称性保护特征或两者兼有的物质阶段进行分类。这将包括零温度间隙量子相和平衡系统中的多体定位（MBL）。 Specific areas of focus include: 1) classifying fermionic symmetry protected phases and understanding the strongly correlated topological surface states they can exhibit, 2) extracting universal properties of topological and symmetry protected phases from commuting projector lattice Hamiltonians and understanding the conditions under which such commuting projector Hamiltonians exist, and 3) classifying topological phases in periodically driven (Floquet) MBL quantum systems. PI将使用分析工具（例如量子场理论和确切的可解决模型）来证明存在段相的存在，并将使用数学方法（例如拓扑量子场理论和代数拓扑学）来研究并可能排除推定的拓扑顺序模式。 PI将开发新的量子信息理论工具来解决这些问题。该项目有可能对拓扑顺序进出平衡的基本了解。特别是，在非平衡MBL系统中对拓扑顺序进行分类的问题不一定与平衡情况相同的现场理论技术适合，但可以用量子信息理论方法来解决。 PI将基于与量子信息社区中的合作者进行持续的工作，以开发此类方法，最近的结果表明，该方法将对物理和量子信息社区都有用。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的审查标准来通过评估来获得支持的。