Order-by-frustration: emergent condensed states of frustrated magnets

该奖项支持磁性绝缘体新状态的理论研究和教育，在这种状态下，局域自旋（包含绕原子核轨道运行的电子的微观磁性成分）之间存在不同种类的相互作用之间的竞争。自旋之间的相互作用可以驱使它们进入磁性有序状态，例如铁磁性，其中电子的自旋沿着相同的公共轴排列，或者反铁磁性，其中相邻的自旋指向相反的方向。这项研究的重点是一类广泛的材料，在这些材料中，由于自旋之间的竞争相互作用，磁顺序似乎完全不存在。然而，更仔细的研究揭示了一种“隐藏”的秩序，在这种秩序中，不是单个的自旋，而是小群自旋在很远的距离上相互关联，远远超过了小群自旋的典型大小。这些类型的秩序被称为多极秩序，本项目致力于对其静态和动态特性进行分类和理解，并了解其实现所需的条件。这项研究促进了对量子力学和磁学的基本理解，特别是在具有不同竞争磁相互作用的材料中。它可能有助于在广泛的材料中发现可能具有技术应用的电子物质的新状态。该奖项还支持理论固体物理学的研究生。参与研究的学生将接受现代理论技术的培训。此外，PI还计划为本科生举办全系物理奥林匹克竞赛。奥林匹克竞赛将由一系列简短但不平凡的问题组成，这些问题需要对一般物理学有很好的理解才能解决。它的目的是促进学生对物理学的兴趣，发现特别有天赋的学生，并为他们提供与专业研究人员的早期接触。该奖项支持理论研究和教育，重点是具有不寻常多粒子凝聚体的受挫磁性材料，以及由于强大和相互竞争的自旋轨道相互作用而出现的“隐藏”受挫系统。该研究汇集了凝聚态物理的几个突出主题-相关系统中竞争顺序的多样性，它们之间的量子相变，以及“隐藏”顺序出现背后的机制识别。不同于通常的单粒子玻色凝聚体，两个（或更多）粒子凝聚体的特征是短程自旋相关和不寻常的向列型有序参数。这方面的例子是一个受挫铁磁体，其相图由一个动力学临界指数为z=4的Lifshitz型量子临界点控制。PI建议建立一个对这一临界点的场论描述，并研究多极自旋向列相出现所需的条件。在这项研究过程中，PI打算探索具有双磁振子凝聚体的玻色子系统与费米子超导体或电荷密度波之间的类比。金属受挫磁体，其中流动电子交换耦合到局域自旋，是PI打算追求的另一个主要研究方向。这些材料允许通过电子传输测量探测磁相和转变的有趣可能性。PI计划从理论上分析经历磁振子玻色-爱因斯坦凝聚跃迁的磁体的电阻率，并将此分析扩展到具有拓扑非平凡带结构的新实验系统。这里发展的理论将应用于实际的磁性材料。通过将场论方法与半经典自旋波展开相结合，PI计划描述最近在kagome材料volborthite中发现的三分之一磁化平台的物理特性，并分析其可能的不稳定性。PI还将研究具有竞争性自旋轨道相互作用的新型自旋链绝缘体，这种绝缘体通过在相邻链中强制相反的螺旋相关性，有效地促进了类似ising的纵向自旋密度波状态，这是流动电子系统中电荷密度波顺序的绝缘模拟。该奖项将支持理论固体物理学的研究生。参与研究的学生将接受玻色子化、重整化群、量子场和图解多体理论等现代理论技术的训练。此外，PI还计划为本科生举办全系物理奥林匹克竞赛。奥林匹克竞赛将由一系列简短但不平凡的问题组成，这些问题需要对一般物理学有很好的理解才能解决。它的目的是促进学生对物理学的兴趣，发现特别有天赋的学生，并为他们提供与专业研究人员的早期接触。

NON-TECHNICAL SUMMARYThis award supports theoretical research and education on new states of magnetic insulators, in which there is a competition between different kinds of interactions between localized spins, the microscopic magnetic components that contain electrons orbiting around atomic nuclei. The interactions between spins can drive them into magnetically ordered states, such as ferromagnetism, in which the spins of the electrons are aligned along the same common axis, or anti-ferromagnetism, in which neighboring spins point in opposite directions. The focus of this research is on a wide class of materials in which magnetic order appears to be altogether absent as a consequence of competing interactions between spins. However, closer examination reveals a kind of "hidden" order, in which not the individual spins but rather small groups of them are correlated over large distances far exceeding the typical size of a small group of spins. These types of order are known as multi-polar, and this project is devoted to classifying and understanding their static and dynamic properties, as well as understanding the conditions necessary for their realization. This research advances fundamental understanding of quantum mechanics and magnetism, particularly in materials with different competing magnetic interactions. It may contribute to the discovery of new states of electronic matter within a wide range materials that may have technological application. This award also supports graduate students in theoretical solid state physics. Students involved in the research will be trained in modern theoretical techniques. In addition, the PI is planning to organize a department-wide Physics Olympiad for undergraduate students. The Olympiad will consist of a set of short but non-trivial problems which requires good understanding of general physics to solve. Its purpose is to promote student interest in physics, to identify particularly talented students and to provide them with early contacts with professional researchers.TECHNICAL SUMMARYThis award supports theoretical investigation and education focused on frustrated magnetic materials with unusual multi-particle condensates as well as on systems with "hidden" frustration which emerges due to strong and mutually competing spin-orbital interactions.The research brings together several outstanding topics of condensed matter physics - the multiplicity of competing orders in correlated systems, quantum phase transitions among them, and identification of the mechanism behind the appearance of "hidden" orders.Unlike the well-understood case of the usual, single particle, Bose condensates, the two (or more)- particle condensates are characterized by short-ranged spin correlations and unusual nematic-type order parameters. The case in point is represented by a frustrated ferromagnet, the phase diagram of which is controlled by a quantum critical point of Lifshitz type with dynamical critical exponent z=4. The PI proposes to construct a field theory description of this critical point, and to investigate the conditions needed for the emergence of multi-polar spin-nematic phases. In the course of this study the PI intends to explore analogies between boson systems with two-magnon condensates and fermion superconductors or charge density waves.Metallic frustrated magnets, in which itinerant electrons are exchange-coupled to localized spins, constitute another major research direction which the PI intends to pursue. These materials allow for the interesting possibility of probing magnetic phases and transitions via electron transport measurements. The PI plans to theoretically analyze the resistivity of a magnet undergoing a magnon Bose-Einstein condensation transition, and also to extend this analysis to novel experimental systems with topologically non-trivial band structures.The theory developed here will be applied to real magnetic materials. By combining a field theory approach with a semi-classical spin wave expansion, the PI plans to describe the physics of the recently discovered one-third magnetization plateau in the kagome material volborthite, and to analyze its possible instabilities. The PI will also study novel spin-chain insulators with competing spin-orbit interactions, which, by forcing opposite helical correlations in the neighboring chains, effectively promote an Ising-like longitudinal spin-density wave state that is an insulating analogue of a charge-density wave order in itinerant electron systems.This award will support graduate students in theoretical solid state physics. Students involved in the research will be trained in modern theoretical techniques such as bosonization, renormalization group, quantum field and diagrammatic many-body theories. In addition, the PI is planning to organize a department-wide Physics Olympiad for undergraduate students. The Olympiad will consist of a set of short but non-trivial problems which requires good understanding of general physics to solve. Its purpose is to promote student interest in physics, to identify particularly talented students and provide them with early contacts with professional researchers.