Topology and Frustration in Spin-Orbit Coupled Quantum Magnets

非技术总结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性状态的理解，在这些材料中，电子可以通过库仑相互作用相互强烈相互作用，并通过其运动和本征磁性与原子核相互作用。这一领域的研究最近在理论和实验上都经历了快速和令人兴奋的发展。新材料的发现和理解是维持技术进步的关键，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焦点将是量子自旋液体的研究。这些都是令人着迷的电子物质状态，在温度绝对零度以下都没有显示出磁性有序的特征。该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，这种量子态可能在合适的条件下出现在多电子相互作用系统中。PI的科学活动的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和更广泛的研究社区的教育活动相结合，包括暑期学校、会议和工作室。技术总结该奖项支持理论研究和教育，以研究在存在强烈的自旋-轨道耦合、非平凡的拓扑和无序的情况下，关联电子的集体行为产生的新的量子相。特别是，PI将专注于开发和分析有效的超级交换哈密顿量来描述Kitaev材料，这些材料在过渡金属氧化物、稀土和卤化物等各种系统中实现。研究小组将计算这些模型的基态相图，并确定可能的量子态和它们之间的相变的性质。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会显著改变磁化过程。研究小组还将研究这些系统中无序的影响，因为无序、挫折和拓扑的竞争可能会导致许多意想不到的现象。PI还将致力于QSL的微观建模，并开发适当的场论方法来描述它们。这项研究将与明尼苏达大学和更广泛的研究社区的教育活动相结合，包括暑期学校、会议和工作坊。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.