Topology and Frustration in Spin-Orbit Coupled Quantum Magnets

该奖项支持理论研究和教育，旨在促进对材料中出现的新型磁态的理解，其中电子可以通过库仑相互作用相互作用，并通过其运动和固有磁性与原子核相互作用。这一研究领域最近在理论和实验方面都有了迅速而令人兴奋的发展。新材料的发现和理解对维持技术进步至关重要，理论和实验之间的密切合作加速了对这些材料的研究。这个项目的一个特别重点将是量子自旋液体的研究。这些都是电子物质的迷人状态，在温度绝对零度以下没有显示出磁有序的特征。研究小组计划阐明涉及量子自旋液体的显著现象，并研究它们在拓扑量子计算中的潜在应用。拓扑量子计算机被设想为通过操纵一种类似粒子的量子态来进行计算，这种量子态可能在多电子相互作用系统的适当条件下出现。PI科学活动更广泛影响的一个重要部分将是指导高级凝聚态物理的博士、硕士和本科生。这项研究将与明尼苏达大学的教育活动以及更广泛的研究社区相结合，包括暑期学校、会议和研讨会。该奖项支持理论研究和教育，以研究在强自旋-轨道耦合、非琐碎拓扑和无序存在下相关电子的集体行为所产生的新量子相。特别是，PI将专注于开发和分析有效的超交换哈密顿量来描述基塔耶夫材料，这种材料可以在各种系统中实现，如过渡金属氧化物、稀土和卤化物。研究小组将计算这些模型的基态相图，并确定它们之间可能的量子态和相变的性质。研究小组还将研究这些模型的有限温度特性和磁场的影响；这些模型中各向异性相互作用的存在往往显著地改变了磁化过程。研究小组还将研究这些系统中无序的影响，因为无序、挫折和拓扑结构的竞争可能会产生许多意想不到的现象。PI还将致力于qsl的微观建模，并开发适当的场理论方法来描述它们。这项研究将与明尼苏达大学的教育活动以及更广泛的研究社区相结合，包括暑期学校、会议和研讨会。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports theoretical research and education that is aimed to advance understanding of novel magnetic states that arise in materials where electrons can interact strongly with each other through the Coulomb interaction and with atomic cores through their motion and intrinsic magnetic properties. This area of research has recently experienced rapid and exciting developments both in theory and in experiment. The discovery and understanding of novel materials are crucial to sustain technological progress, and close work between theory and experiment has accelerated research on these materials. A particular focus of this project will be the study of quantum spin liquids. These are fascinating states of electron matter which show no signatures of magnetic ordering down to the absolute zero of temperature. The research team plans to elucidate remarkable phenomena involving quantum spin liquids, and to investigate their potential applications for topological quantum computation. Topological quantum computers are envisioned to do computation by manipulating a kind of particle-like quantum state that may emerge under the right conditions in interacting systems of many-electrons. An important part of the broader impact of the PI's scientific activity will be mentoring PhD, Master and undergraduate students in advanced condensed matter physics. The research will be integrated with educational activities at the University of Minnesota and in the broader research community, including summer schools, conferences, and workshops.TECHNICAL SUMMARYThis award supports theoretical research and education to study novel quantum phases arising from collective behavior of correlated electrons in the presence of strong spin-orbit coupling, non-trivial topology, and disorder. In particular, the PI will focus on the development and analysis of effective super-exchange Hamiltonians to describe Kitaev materials, which are realized in a variety of systems such as transition metal oxides, rare-earths, and halides. The research team will compute ground state phase diagrams of these models and identify the nature of possible quantum states and phase transitions among them. The research team will also study finite temperature properties of these models and the effects of magnetic field; the presence of anisotropic interactions in these models often significantly modifies the magnetization processes. The research team will also study the effects of disorder in these systems, as the competition of disorder, frustration and topology can potentially give rise to many unexpectedphenomena. PI will also be working on the microscopic modeling of QSLs and developing of appropriate field-theoretical methods to describe them. The research will be integrated with educational activities at the University of Minnesota and in the broader research community, including summer schools, conferences, and workshops.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.