Applications of Field Theory to Condensed Matter Physics

场论在凝聚态物理中的应用

• 批准号: 1725401
• 负责人: Eduardo Fradkin
• 金额: $ 66万
• 依托单位: University of Illinois at Urbana-Champaign
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-09-01 至 2022-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1725401&HistoricalAwards=false
• 关键词: Applications; Field; Theory; Condensed; Matter

NONTECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding condensed matter systems whose behavior is governed by strong effects of quantum mechanics and strong interactions between their constituent electrons. Such understanding could lead to the prediction of new states of matter with novel properties as well as to the discovery of new materials with potentially useful applications. The PI and his collaborators have predicted the existence of strongly interacting quantum states of matter, named intertwined orders, in which electrons organize themselves in complex patterns. Intertwined orders describe physical systems in which, due to the strong interactions between the constituent electrons, different and seemingly competing types of organization coexist and emerge together with nearly equal strength. Superconductors are a relevant example. These are materials in which, at sufficiently low temperatures, electrons enter a cooperative quantum mechanical state that enables them to conduct electricity without any resistance. High-temperature superconductors are a particularly interesting species because they exhibit superconductivity at much higher temperatures than many other known classes of superconductors. The PI's proposed state of matter may help explain how this is possible, and how materials that exhibit superconductivity at room temperature might be discovered. This could lead to virtually lossless transmission of electric power and other energy-related applications. The other focus of the research concerns the understanding of new states of matter, called topological phases, which are essentially immune to the usually destructive effects that disorder and other defects have on material properties. Topological phases are predicted to have unusual properties that could enable computation based on the laws of quantum mechanics. A quantum computer could solve certain problems much faster than any currently existing computer.  The research involves cutting-edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices. Research and education will be further integrated through the development of advanced curricular materials.TECHNICAL SUMMARYThis award supports theoretical research and education aimed at understanding condensed matter systems involving many strongly coupled degrees of freedom whose behavior is governed by strong effects of quantum mechanics. The electrons in such strongly correlated systems organize spontaneously in electronic liquid-crystal phases and in topological phases. An unavoidable feature of these phases is that they naturally describe intertwined orders. The main focus of the project is on the theory of intertwined orders in strongly correlated systems, and on topological phases of matter. Both lines of research require the development of new theoretical insights and the use of methods and ideas from quantum field theory. The projects include studies of the emergence of pair-density-wave superconducting states in microscopic models, both in a quasi-one-dimensional setting and in ladder systems, developing an effective field theory of pair-density-wave and charge 4e superconducting states, and uncovering the mechanism connecting electronic nematic order and superconductivity. The PI's work on topological phases of matter aims to establish a relation between electronic nematic order and paired quantum Hall states (a form of intertwined orders), and to develop the lattice Chern-Simons gauge theory of frustrated quantum antiferromagnets, with applications to the theory of fractionalized Chern insulators. An important new project aims at finding a relation between the theory of quantum critical loops that the PI developed earlier and the recently conjectured quantum dualities for Dirac systems.The research involves cutting-edge problems in the physics of materials and provides excellent opportunities to train the next generation of theoretical scientists. It also opens new possibilities for future technologies related to advanced solid-state materials for electronic devices. Research and education will be further integrated through the development of advanced curricular materials.

非技术性总结该奖项支持理论研究和教育，旨在了解凝聚态系统，其行为受量子力学的强烈影响及其组成电子之间的强烈相互作用的影响。这种理解可能会导致预测具有新特性的新物质状态，以及发现具有潜在有用应用的新材料。PI和他的合作者预测了物质的强相互作用量子态的存在，称为交织秩序，其中电子以复杂的模式组织自己。互扰有序描述的是这样一种物理系统，在这种系统中，由于组成电子之间的强相互作用，不同的、看似竞争的组织类型共存，并以几乎相等的强度出现。超导体就是一个相关的例子。在这些材料中，在足够低的温度下，电子进入合作的量子力学状态，使它们能够在没有任何电阻的情况下导电。高温超导体是一个特别有趣的物种，因为它们在比许多其他已知类别的超导体高得多的温度下表现出超导性。PI提出的物质状态可能有助于解释这是如何可能的，以及如何发现在室温下表现出超导性的材料。这可能导致电力和其他能源相关应用的几乎无损传输。该研究的另一个重点是理解新的物质状态，称为拓扑相，它基本上不受无序和其他缺陷对材料性质的破坏性影响。拓扑相被预测具有不寻常的性质，可以根据量子力学定律进行计算。量子计算机可以比现有的任何计算机更快地解决某些问题。这项研究涉及材料物理学的前沿问题，并为培养下一代理论科学家提供了绝佳的机会。它还为与电子设备的先进固态材料相关的未来技术开辟了新的可能性。通过开发先进的课程材料，研究和教育将进一步结合起来。技术总结该奖项支持理论研究和教育，旨在理解涉及许多强耦合自由度的凝聚态系统，其行为受量子力学的强烈影响。在这种强关联系统中的电子自发地组织在电子液晶相和拓扑相。这些阶段的一个不可避免的特征是，它们自然地描述了相互交织的秩序。该项目的主要重点是强相关系统中交织秩序的理论，以及物质的拓扑相。这两条研究路线都需要发展新的理论见解，并使用量子场论的方法和思想。这些项目包括研究准一维和梯形系统中微观模型中成对密度波超导态的出现，发展成对密度波和电荷4 e超导态的有效场论，以及揭示电子有序和超导性之间的联系机制。PI在物质拓扑相方面的工作旨在建立电子有序和成对量子霍尔态（一种交织有序的形式）之间的关系，并发展受抑量子反铁磁体的格点陈-西蒙斯规范理论，并应用于分形陈绝缘体理论。一项重要的新项目旨在发现PI早期开发的量子临界回路理论与最近发现的狄拉克系统量子对偶之间的关系，该研究涉及材料物理学的前沿问题，并为培养下一代理论科学家提供了极好的机会。它还为与电子设备的先进固态材料相关的未来技术开辟了新的可能性。将通过编制先进的教材，进一步将研究和教育结合起来。

项目成果

Fractionalizing global symmetry on looplike topological excitations

环状拓扑激励上的全局对称性的分数化

• DOI: 10.1103/physrevb.105.205137
• 发表时间: 2022
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Ning, Shang-Qiang;Liu, Zheng-Xin;Ye, Peng
• 通讯作者: Ye, Peng

Helical spin thermoelectrics controlled by a side-coupled magnetic quantum dot in the quantum spin Hall state

• DOI: 10.1103/physrevb.98.195429
• 发表时间: 2018-11-19
• 期刊: PHYSICAL REVIEW B
• 影响因子: 3.7
• 作者: Roura-Bas, Pablo;Arrachea, Liliana;Fradkin, Eduardo
• 通讯作者: Fradkin, Eduardo

Thermalization of randomly coupled SYK models

• DOI: 10.1088/1742-5468/ac416b
• 发表时间: 2021-09
• 期刊: Journal of Statistical Mechanics: Theory and Experiment
• 作者: R. Sohal;L. Nie;Xiao-Qi Sun;E. Fradkin

Topology and the one-dimensional Kondo-Heisenberg model

拓扑和一维近藤-海森堡模型

• DOI: 10.1103/physrevb.101.165133
• 发表时间: 2020
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: May-Mann, Julian;Levy, Ryan;Soto-Garrido, Rodrigo;Cho, Gil Young;Clark, Bryan K.;Fradkin, Eduardo
• 通讯作者: Fradkin, Eduardo

Generalized Wen-Zee terms

• DOI: 10.1103/physrevb.99.205120
• 发表时间: 2018-07
• 期刊: Physical Review B
• 影响因子: 3.7
• 作者: Bolin Han;Huajia Wang;P. Ye