Computational Studies of Entanglement and Thermodynamics of Strongly Interacting Spin Systems

该奖项支持材料中物质新相的理论和计算建模。从磁铁到金属，再到半导体和超导体，这些材料的特性是由电子在给定材料的复杂晶体环境中运动决定的，并且由于量子力学和静电库仑相互作用的原理而相互合作。新的电子态可以从电子的相关运动中产生。PI将研究材料模型中的电子相位，这些模型可以：(i)提供关于大量电子复杂合作行为如何产生新现象和特性的见解，以及（ii）为实验科学家提供可能的材料，这些材料的特性可以通过新颖的方式进行外部控制，从而允许各种设备和应用。要研究的电子相的例子包括高温超导体中的电子相、接近于从金属转变为绝缘体的系统，以及表现出不寻常磁性形式的材料。虽然主要关注材料现象的研究，但该项目与量子场论、甚至几何、拓扑学和量子引力的基础有着深刻的联系。该项目的教育部分包括训练计算物理领域的研究生和高级本科生，使其具备在所有科学和工程领域广泛有用的技能。它还包括通过加州大学的加州数学和科学暑期学校项目与高中生互动，在那里PI将开发和教授适合这些学生的课程。该奖项支持材料中物质的新型电子相的理论和计算建模。量子力学是我们对固体物理学理解的基础。这个项目涉及奇异的量子相，它违背了传统的多电子行为范式。电子和它们的自旋之间强烈竞争的相互作用会导致挫折和奇异的量子相，在那里可以出现新的自由度。PI将特别关注现实磁性材料中具有竞争性或令人沮丧的交换相互作用的物质的新量子相的存在。这样的相位可以支持在其他地方找不到的材料内部的涌现场和粒子。PI将使用高温级数展开和数值链接簇展开，对适当模型的热力学和光谱特性进行系统计算，包括有和没有淬火无序。这将有助于建立模型和材料之间的联系。要研究的系统包括量子自旋冰材料和Kagome-Lattice海森堡系统。PI将与实验小组合作，了解铁镍材料中的非常规超导现象，钛酸钇等稀土焦绿石中的量子自旋冰行为和新兴量子电动力学，以及kagome和三角形晶格反铁磁体中的量子自旋液体。该项目的另一个重点是研究多体系统中的量子纠缠。使用级数展开方法，PI将计算各种格统计模型中的基态纠缠熵。这些计算应该对量子相变和临界现象、费米表面几何和物质的拓扑相提供信息。此外，本学科还与量子信息论、量子场论、几何、拓扑学甚至量子引力有着深刻的联系。该项目的教育部分包括对研究生和本科生进行理论和计算物理方法的培训，这些方法应在科学和工业中广泛使用。此外，PI将通过加州大学的加州数学和科学暑期学校项目与有才华的高中生合作，并通过物理和数学科学项目的本科生研究参与者指导与代表性不足的学生合作。

NONTECHNICAL SUMMARYThis award supports theoretical and computational modeling of novel phases of matter in materials. From magnets to metals to semiconductors and superconductors, the properties of these materials are determined by electrons moving in the intricate crystalline environment of a given material and cooperating with each other due to the principles of quantum mechanics and electrostatic Coulomb interactions. New electronic states can emerge from the correlated motion of electrons. The PI will study phases of electrons in models for materials that can: (i) provide insight into how new phenomena and properties emerge as a result of complex cooperative behavior of a large number of electrons, and (ii) present experimental scientists with possible materials with properties that can be controlled externally in novel ways, allowing for various devices and applications. Examples of electronic phases to be studied include those in high temperature superconductors, systems that are close to transforming from a metal to an insulator, and materials that exhibit unusual forms of magnetism. While focused primarily on the study of phenomena in materials, this project has deep connections with fundamentals of quantum field theory and even geometry, topology and quantum gravity.Educational components of this project involve training graduate and advanced undergraduate students in the areas of Computational Physics, with skills that would be broadly useful over all areas of science and engineering. It would also involve interacting with high school students through the California Summer School for Math and Science program of the University of California, where the PI would develop and teach courses suitable for these students. TECHNICAL SUMMARYThis award supports theoretical and computational modeling of novel electronic phases of matter in materials. Quantum mechanics underlies much of our understanding of solid state physics. This project deals with exotic quantum phases that defy conventional paradigms of many-electron behavior. Strongly competing interactions between electrons and their spins can lead to frustration and exotic quantum phases, where new degrees of freedom can emerge. The PI will focus particularly on the existence of novel quantum phases of matter in real magnetic materials with competing or frustrating exchange interactions. Such phases can support emergent fields and particles inside the materials that are not found elsewhere. The PI will pursue systematic calculations of thermodynamic and spectral properties of appropriate models, with and without quenched disorder using high-temperature series expansions and numerical linked cluster expansions. This will help establish the connection between models and materials. Systems to be studied include quantum spin-ice materials and Kagome-Lattice Heisenberg systems. The PI will work with experimental groups to understand such phenomena as unconventional superconductivity in the iron-pnictide materials, quantum spin-ice behavior and emergent quantum electrodynamics in rare-earth pyrochlores such as ytterbium titanate, and quantum spin-liquids in kagome and triangular lattice antiferromagnets.Another focus of the project is the study of quantum entanglement in many-body systems. Using series expansion methods, the PI will calculate ground state entanglement entropies in various lattice-statistical models. These calculations should be informative about quantum phase transitions and critical phenomena, Fermi-surface geometry and topological phases of matter. In addition, this subject also has deep connections with quantum information theory, quantum field theory, geometry, topology and even quantum gravity.Educational components of the project involve training graduate and undergraduate students in methods of theoretical and computational physics that should be broadly useful in science and industry. In addition the PI will work with talented high school students through the California Summer School for Math and Science program of the University of California and with underrepresented students through the Mentorship for Undergraduate Research Participants in the Physical and Mathematical Sciences program.