Frustrated Magnetism in Triangular Geometries with Heisenberg and Multi-spin Ring Exchanges

该奖项支持理论和计算研究和教育，以识别和理解物质的新型量子相的特性。强受挫二维磁性材料为许多新相提供了候选体系。它们可以表现为磁性有序相、价键晶体相、共振价键相以及无间隙或代数自旋液相。其中一些相和它们之间的量子相变可能导致具有分数量子数的新型粒子，这是我们的凝聚态物理标准模型无法理解的。在实际材料中对这些阶段的明确演示仍然是一个非常活跃的研究领域，也是本工作的主要焦点。PI的目标是模拟几种准二维材料的受挫磁性行为，如石墨上吸收的氦-3层、有机分子晶体和最近发现的基于kagome晶格的赫伯特史密斯石。在过去的十年里，PI开发了链接簇技术，使人们能够高精度地计算量子晶格模型的热力学和光谱特性。这些计算应该有助于发展对这些系统的全面理解。拟议的活动将包括培训从高中到研究生水平的新一代科学家。除了与研究生密切合作外，PI还将通过加州大学戴维斯分校物理科学项目的少数民族本科生研究参与指导本科生，特别是少数民族本科生。此外，PI将继续通过加州大学的加州州立数学和科学暑期学校项目培训有天赋的高中生。PI将为更广泛的社区开发一个可网络访问的量子晶格模型光谱特性存储库。将组织一个跨学科的研讨会，主题是分子挫折科学的普遍主题，将汇集来自不同领域的科学家，包括磁力，玻璃和蛋白质折叠。该奖项支持研究和教育，以识别和理解物质的新型量子相的特性。PI将使用理论方法和计算机模拟来观察材料中最小的磁性单位是否能形成一种类似于一种特殊液体——量子液体的物质状态。大多数液体冷却到足够低的温度时，就会冻结成固体。一个明显的例外是氦元素，它在一般条件下一直保持液态直至绝对零度。当磁性材料冷却时，原子尺度上最小的磁性单位（通常是单个电子）的南北两极会自发地排列成一块磁铁。但是，是否有一些材料，这些微小的磁体在它们的波动中表现出某种相关性，但即使在温度降到绝对零度时也不会形成磁性状态？这种被称为自旋液体的性质是什么？PI试图回答这个问题。人们相信，了解自旋液体可能形成的条件及其性质可能会导致发现新的物质状态，例如超导状态，能够导电而不会损失，或者物质的奇异量子力学状态，可以很容易地操纵，形成高性能超级计算机的操作基础。这项研究将提供教育经验，以帮助培养学生从研究生到高中的水平。在过去的几年里，PI一直在为加利福尼亚的高中生开发和教授一门课程，该课程涉及随机漫步及其与物理、化学和生物学中分子基本特性的关系。PI计划在这样的课程中以非常简单的术语结合量子物理学的先进思想。PI还计划组织跨学科会议，将量子磁学领域的新思想推广到其他领域，这些领域的微观挫折或竞争有序趋势发挥着重要作用，如玻璃物理学和蛋白质折叠。PI将为更广泛的社区开发一个可访问网络的研究计算结果存储库。

TECHNICAL SUMMARYThis award supports theoretical and computational research and education to identify and understand properties of novel quantum phases of matter.Strongly frustrated two-dimensional magnetic materials provide candidate systems for many novel phases. They can exhibit magnetically ordered phases, Valence Bond Crystal phases, Resonating Valence Bond phases as well as gapless or algebraic spin-liquid phases. Several of these phases and quantum phase transitions between them may lead to new types of particles with fractional quantum numbers, which cannot be understood from our standard models of condensed matter physics. A definitive demonstration of such phases in real materials remains a very active area of study and is the primary focus of this work.The PI aims to model frustrated magnetic behavior of several quasi-two dimensional materials, such as Helium-3 layers absorbed on graphite, organic molecular crystals and recently discovered kagome-lattice based Herbertsmithites. Over the past decade the PI has developed Linked Cluster techniques that allow one to calculate thermodynamic and spectral properties of quantum lattice models with high accuracy. These calculations should help develop a comprehensive understanding of these systems.The proposed activity would involve training the new generation of scientists from high school to graduate levels. In addition to working closely with graduate students, the PI will mentor undergraduate students, especially minority undergraduate students through the Minority Undergraduate Research Participation in the Physical Sciences program at UC Davis. In addition, the PI will remain engaged in training gifted high school students through the California State Summer School for Mathematics and Science program of University of California.The PI will develop a web-accessible repository of spectral properties of quantum-lattice models for the broader community. An interdisciplinary workshop will be organized on Universal Themes in the Science of Molecular Frustration that will bring together scientists from diverse fields including magnetism, glasses and protein-folding.NONTECHNICAL SUMMARYThis award supports research and education to identify and understand properties of novel quantum phases of matter.The PI will use theoretical methods and computer simulation to see if the tiniest units of magnetism in a material can form a state of matter that is analogous to a peculiar kind of liquid, a quantum liquid. Most liquids, when cooled to sufficiently low temperatures, will freeze into a solid. A notable exception is the element Helium which under ordinary conditions remains a liquid down to the absolute zero of temperature. As a magnetic material is cooled, the north and south poles of the smallest units of magnetism at the atomic scale, often individual electrons, spontaneously align to form a magnet. But are there materials for which these tiny magnets exhibit some correlation in their fluctuations but never form a magnetic state even down to the absolute zero of temperature. What would be the properties of this spin-liquid as it is called? The PI seeks to answer this question. It is believed that understanding the conditions under which spin-liquids might form and their properties may lead to the discovery of new sates of matter, for example a superconducting state, that is able to conduct electricity without loss, or exotic quantum mechanical states of matter that may be easily manipulated to form the basis of operation for a high performance supercomputer.This research will provide educational experiences to help train students from graduate to high school levels. The PI has been involved over the last several years in developing and teaching a course for high school students in California dealing with random walks and their relation to essential properties of molecules in physics, chemistry and biology. The PI plans to incorporate advanced ideas of quantum physics in very simple terms in such courses. The PI also plans to organize interdisciplinary meetings to promote new ideas from the field of quantum magnetism to other fields where microscopic frustration or competing ordering tendencies play an important role such as the physics of glasses and protein-folding. The PI will develop a web-accessible repository of computational results of the research for the broader community.