Quantum Spin-Orbital Systems: Models and Spectroscopies

该奖项支持理论和计算研究以及旨在促进我们对量子系统的理解的教育活动，其中自旋和轨道自由度是强耦合的。相关材料是受挫晶格上的过渡金属氧化物。这项研究分为两部分。第一部分研究了具有自旋和轨道涨落耦合的强相互作用电子系统的基本性质。钒酸盐可能是自旋轨道系统中最突出的例子。这一部分的研究是基于最近对几种钒酸盐的实验，包括尖晶石ZnV2O4和准一维CaV2O4，其中由于特殊的轨道相互作用结构而出现了维数的降低。PI将研究相关的一维自旋轨道系统。这些化合物中的钒链具有磁相互作用受阻、类似伊辛的轨道交换和较大的相对论性自旋轨道相互作用的特点。相应的一维自旋轨道系统在许多方面与著名的一维SU(4)模型不同。PI打算使用分析和数值理论技术来研究这些模型，包括玻色子化和密度矩阵重整化群。第二部分讨论了自旋轨道耦合系统中双磁振子和双轨道拉曼散射理论的发展。这是一个具有挑战性但有益的项目，因为该理论可以很容易地应用于理解具有耦合自旋和轨道自由度的相关材料的各种现有实验数据。我们将特别强调反铁磁体、轨道有序态和自旋轨道液体在受挫晶格上的拉曼散射。PI将从事研究生一级的教育活动，目的是改进和加强固态、统计和多体物理学的课程。她将开设一门关于复杂系统中强相关现象的高级课程，特别强调磁和输运现象的新趋势。一名研究生将参与这项研究活动。PI将与威斯康星大学麦迪逊分校的其他教师合作，组织一个威斯康星冬季学校，研究现代凝聚态物质和量子信息，这将向年轻的研究人员介绍该领域的各种问题，并将改善威斯康星大学系统所有校区的教师、学生和博士后之间的合作。该奖项支持理论和计算研究以及教育活动，旨在提高我们对材料的理解，其中电子自旋，电子固有的量子力学性质，以及电子的运动彼此强烈相互作用。相关材料是氧化物，包括过渡金属，例如钒或锌，原子的某些空间排列导致电子的自旋或空间分布，这可能以许多几乎相等的方式发生，因此，竞争的方式。从理论上理解这些强相关材料的性质是具有挑战性的。对这些系统的兴趣部分来自于它们丰富的新特性：意想不到的各种有序状态，如各种形式的磁性，它们之间的转换，以及它们对应力的敏感性，如外加电场或磁场。PI将使用最先进的分析和计算工具来研究这些过渡金属氧化物的物理性质，预测这些材料的新效应，并有助于理解实验。PI将从事研究生一级的教育活动，目的是改进和加强固态、统计和多体物理学的课程。她将开设一门关于复杂系统中强相关现象的高级课程，特别强调磁和电子输运现象的新趋势。一名研究生将参与这项研究活动。PI将与威斯康星大学麦迪逊分校的其他教师合作，组织一个威斯康星冬季学校，研究现代凝聚态物质和量子信息，这将向年轻的研究人员介绍该领域的各种问题，并将改善威斯康星大学系统所有校区的教师、学生和博士后之间的合作。

TECHNICAL SUMMARY This award supports theoretical and computational research and educational activities aimed at advancing our understanding of quantum systems, in which spin and orbital degrees of freedom are strongly coupled. Relevant materials are transition metal oxides on frustrated lattices. The research has two parts. The first part is devoted to the study of the fundamental properties of strongly interacting electron systems with coupled spin and orbital fluctuations. Vanadates are perhaps the most prominent examples of spin-orbital systems. The research in this part is motivated by recent experiments on several vanadates including spinel ZnV2O4 and quasi one-dimensional CaV2O4, in which reduced dimensionality appears because of a particular structure of orbital interactions. The PI will study relevant one-dimensional spin-orbital systems. The vanadium chains in these compounds are characterized by frustrated magnetic interactions, Ising-like orbital exchanges, and a large relativistic spin-orbit interaction. Corresponding one-dimensional spin-orbital systems are in many aspects different from the famous one-dimensional SU(4) model. The PI intends to investigate these models using both analytical and numerical theoretical techniques, including bosonization and density matrix renormalization group. The second part of the proposal is devoted to the development of the theory of two-magnon and two-orbiton Raman scattering in coupled spin-orbital systems. This is a challenging but rewarding project as the theory can be readily applied to understanding a variety of existing experimental data in correlated materials with coupled spin and orbital degrees of freedom. Special emphasis will be given to the study of Raman scattering from antiferromagnets, orbitally ordered states, and spin-orbital liquids on frustrated lattices. The PI will be engaged in educational activities at the graduate level aimed at refining and enhancing courses in solid state, statistical and many-body physics. She will develop an advanced course in strongly correlated phenomena in complex systems with special emphasis on new trends in magnetism and transport phenomena. A graduate student will be involved in the research activity. The PI will organize, in collaboration with other faculty from UW-Madison, a Wisconsin Winter School on Modern Condensed Matter and Quantum Information, which will introduce young researchers to various problems in the field and will also improve collaboration between faculty, students, and postdocs from all campuses of the University of Wisconsin system. NONTECHNICAL SUMMARY This award supports theoretical and computational research and educational activities aimed at advancing our understanding of materials, in which the electron spin, an intrinsic quantum mechanical property of electrons, and the motion of the electron strongly interact with each other. The relevant materials are oxides that include transition metals, for example vanadium or zinc, with certain spatial arrangements of atoms leading to spin or spatial distribution of electrons which can occur in many nearly equivalent and hence, competing ways. Achieving a theoretical understanding of the properties of these strongly correlated materials is challenging. Interest in these systems stems in part from the richness of their novel properties: the unexpected variety of ordered states, like various forms of magnetism, the transformations among them, and their sensitivity to stresses, such as applied electric or magnetic fields. The PI will use state-of-the-art analytical as well as computational tools to investigate the physical properties of such transition metal oxides, predict new effects in these materials, and contribute to understanding of experiments. The PI will be engaged in educational activities at the graduate level aimed at refining and enhancing courses in solid state, statistical and many-body physics. She will develop an advanced course in strongly correlated phenomena in complex systems with special emphasis on new trends in magnetism and electron transport phenomena. A graduate student will be involved in the research activity. The PI will organize, in collaboration with other faculty from UW-Madison, a Wisconsin Winter School on Modern Condensed Matter and Quantum Information, which will introduce young researchers to various problems in the field and will also improve collaboration between faculty, students, and postdocs from all campuses of the University of Wisconsin system.