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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.

非技术摘要该奖项支持关于凝聚态物质系统的奇异低温状态的理论研究和教育。尽管量子力学在微观层面描述了物质的行为，但量子力学效应在宏观尺度上通常是不可见的。 20 世纪 80 年代，在研究量子霍尔效应时发现了一种新的所谓“拓扑有序”态，其中电子被限制在两个半导体之间的平面内，并置于垂直于该平面的高磁场中。量子霍尔态显示出在宏观尺度上可以感受到的量子效应。其中包括仅携带一小部分电子电荷的粒子状行为和仅允许电荷沿一个方向流动的通道的出现。为了更好地了解材料中可以实现哪些类型的新电子态以及如何通过实验检测它们，PI和合作者将结合理论凝聚态物理和量子信息论领域的方法，量子信息论领域由信息论、量子力学、数学和信息论的思想组成。计算机科学。量子信息论提供了一种有效的方法来思考涉及量子力学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聚态物理学前沿的研究生教育。此外，PI 将继续开发研究生水平课程，除了标准凝聚态场理论之外，还结合了量子信息论的新材料。此外，这项工作可能会产生额外的积极影响，因为凝聚态物质的想法可能会导致量子信息和量子计算的进步。技术摘要该奖项支持关于强相关多体量子系统中对称性和拓扑的综合效应的理论研究和教育。这种强相关系统可以实现超越标准金兹堡-朗道-威尔逊对称性破缺范式的物质零温度相。这些可以具有内在的拓扑顺序并支持分段“任意子”激发，或者它们可以受到对称性保护。该项目的很大一部分将是对表现出内在拓扑顺序、对称性保护特征或两者的物质相进行分类。这将包括平衡零温带隙量子相和多体局域（MBL）非平衡系统。具体重点领域包括：1）对费米子对称保护相进行分类并了解它们可以表现出的强相关拓扑表面态，2）从交换投影晶格哈密顿量中提取拓扑和对称保护相的通用性质并了解此类交换投影哈密顿量存在的条件，以及3）对周期性驱动（Floquet）MBL量子系统中的拓扑相进行分类。 PI 将使用量子场论和精确可解模型等分析工具来证明有隙相的存在，还将使用拓扑量子场论和代数拓扑等数学方法来研究并可能排除拓扑序的假定模式。 PI 将开发新的量子信息理论工具来解决这些问题。该项目有潜力发展对平衡状态和非平衡拓扑顺序的基本理解。特别是，非平衡 MBL 系统中拓扑序的分类问题不一定适用于平衡情况下相同的场论技术，但可以通过量子信息论方法有效解决。该 PI 将与量子信息界的合作者持续合作开发此类方法，最近的结果表明这些方法对物理学界和量子信息界都有用。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。