Quantum Monte Carlo Simulations of Quantum Criticality and Topological Phases

该奖项支持理论和计算研究，以及教育，以促进对量子材料的理解，这些材料涉及费米子系统中的量子临界，量子相变的非相干起源，以及自旋轨道耦合和强相关性存在下的新兴拓扑相。PI的一般方法是开发包含上述现象本质的模型，并通过各种方法（包括量子蒙特卡罗模拟）来研究它们。这项研究也对超冷原子气体领域产生了影响，该领域已成为深入了解量子材料的优秀实验室。PI希望在这个项目过程中取得的重大突破是：(i)对费米表面和相关准粒子激发如何在量子临界点附近被破坏的定量理解；（ii）理解耗散的起源和在量子相变附近出现新的导电但不相干的金属相；（iii）在具有自旋-轨道耦合和强相关性的系统中出现具有非平凡空间、自旋和拓扑有序的超流体；（iv）一个完全开发的最先进的QMC代码库，包括(a)蠕虫算法和最大熵方法，用于大规模玻色子模拟，提供有关动态敏感性的信息；(b)基于波函数的大参数优化变分蒙特卡罗方法；(c)声誉QMC方法，最小化对波函数的依赖。该项目还支持培养学生在一个多样化的研究小组的背景下工作，以促进对量子物质和材料的理解。PI计划在哥伦布科学博物馆举办以随机数“葡萄干到PI”为主题的物理节。PI在哥伦布市学区的Innis小学率先开展了“遇见科学家，成为科学家，了解其他科学家”的科学思考者项目。PI将推出一个本科教育网站，提供10分钟的简短讲座片段，可供搜索，并将她的努力与其他远程教育选择相协调。非技术摘要：该奖项支持理论和计算研究，以及关于物质的新涌现状态和它们之间的量子相变的教育。材料是由许多电子和离子组成的，它们之间的相互作用导致了物质的新状态，比如超导体和磁铁，它们是由电子的自组织、它们的运动和它们被称为自旋的内在磁性取向产生的。PI将研究当电子的自旋被锁定在它的运动中时，新相位可能出现的可能性。当粒子之间的相互作用强到足以支配它们的运动能量时，它们的动能，具有刺猬，漩涡和螺旋结构的织构磁相可能会产生。电子在磁性结构的背景下运动，导致了与电子输运有关的材料的不寻常性质。PI还将探索量子相变。这些是发生在绝对零度的相变。据信，这些转变可能产生的后果可能达到室温的很大一部分。与我们所熟悉的由热涨落驱动的水到蒸汽的相变不同，量子相变是由海森堡著名的测不准原理引起的量子涨落驱动的。量子相变可能会导致剧烈的变化，比如改变粒子之间的相互作用，或者施加磁场或压力，将一个量子态重构为完全不同的量子态。这些至关重要的问题将在物理模型的背景下进行探讨，这些模型与包含过渡金属的氧化物材料以及被困于光晶格中的超冷原子直接相关。该项目还支持培养学生在一个多样化的研究小组的背景下工作，以促进对量子物质和材料的理解。PI计划在哥伦布科学博物馆举办以随机数“葡萄干到PI”为主题的物理节。PI在哥伦布市学区的Innis小学率先开展了“遇见科学家，成为科学家，了解其他科学家”的科学思考者项目。PI将推出一个本科教育网站，提供10分钟的简短讲座片段，可供搜索，并将她的努力与其他远程教育选择相协调。

TECHNICAL SUMMARYThis award supports theoretical and computational research, and education to advance understanding of quantum materials pertaining to quantum criticality in fermionic systems, the origin of incoherence across quantum phase transitions, and emergent topological phases in the presence of spin-orbit coupling and strong correlations. The PI's general approach is to develop models that contain the essence of the phenomena mentioned above, and to investigate them by a variety of methods, including quantum Monte Carlo simulations. This research also has impact on the field of ultracold atomic gases that have emerged as excellent laboratories for gaining insights into quantum materials. Major breakthroughs that the PI hopes to make in the course of this project are:(i) a quantitative understanding of how a Fermi surface and associated quasiparticle excitations are destroyed near a quantum critical point;(ii) an understanding of the origin of dissipation and emergence of novel conducting but incoherent metallic phases near a quantum phase transition;(iii) emergence of a superfluid with non-trivial spatial, spin and topological ordering in a system with spin-orbit coupling and strong correlations;(iv) a library of fully developed state-of-the-art QMC codes, including (a) worm algorithm and maximum entropy methods for large-scale boson simulations providing information about dynamical susceptibilities; (b) wavefunction based variational Monte Carlo methods with optimization of large numbers of parameters; and (c) reputation QMC methods that minimize the dependence on the wavefunction.This project also supports training students in the setting of a diverse research group working to advance understanding of quantum matter and materials. The PI plans to organize a Festival of Physics at the Columbus Science Museum on the theme of random numbers "Raisins to Pi." The PI is spearheading the Scientific Thinkers program Meet a Scientist, Be a Scientist, and Learn about other Scientists at the Innis Elementary School in the Columbus City School district. The PI will launch a website for undergraduate-level education with short 10 minute lecture-nuggets that are searchable and coordinate her efforts with other options for distance learning. Non-Technical abstract:This award supports theoretical and computational research, and education on novel emergent states of matter and on quantum phase transitions between them. Materials are made up of many electrons and ions and the interactions among them lead to new states of matter, such as superconductors and magnets, which arise from the self-organization of the electrons, their motion, and their intrinsic magnetic orientation known as spin. The PI will investigate the possibility that novel phases could emerge when the spin of the electron is locked to its motion. When interactions between the particles are strong enough to dominate over the energy due to their motion, their kinetic energy, textured magnetic phases with hedgehog, vortex and spiral structures may result. Electrons moving in the background of magnetic textures lead to unusual properties of materials related to the transport of electrons. The PI will also explore quantum phase transitions. These are phase transformations that take place at the absolute zero of temperature. It is believed that these transitions may have consequences that may reach up to a significant fraction of room temperature. Unlike the familiar phase transformation from water to steam which is driven by thermal fluctuations, quantum phase transitions are driven by quantum fluctuations which arise from Heisenberg's famous uncertainty principle. Quantum phase transitions may lead to dramatic changes such as the restructuring of one quantum state to a completely different one upon changing the interactions between particles, or the application of a magnetic field, or pressure. These questions of fundamental importance will be explored in the context of physical models that have direct relevance to oxide materials containing transition metal as well as ultracold atoms in trapped in lattices of light. This project also supports training students in the setting of a diverse research group working to advance understanding of quantum matter and materials. The PI plans to organize a Festival of Physics at the Columbus Science Museum on the theme of random numbers "Raisins to Pi." The PI is spearheading the Scientific Thinkers program Meet a Scientist, Be a Scientist, and Learn about other Scientists at the Innis Elementary School in the Columbus City School district. The PI will launch a website for undergraduate-level education with short 10 minute lecture-nuggets that are searchable and coordinate her efforts with other options for distance learning.