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，以促进对与费米系统中的量子临界性有关的量子材料的理解，量子相变中不相干的起源，以及存在自旋轨道耦合和强相关性的新兴拓扑相。PI的一般方法是开发包含上述现象本质的模型，并通过各种方法进行研究，包括量子蒙特卡罗模拟。这项研究也对超冷原子气体领域产生了影响，这些气体已经成为深入了解量子材料的优秀实验室。PI希望在这个项目中取得的主要突破是：（i）对费米面和相关准粒子激发在量子临界点附近如何被破坏的定量理解;（ii）对耗散的起源和量子相变附近新的导电但不相干的金属相的出现的理解;（iii）在具有自旋轨道耦合和强关联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）一个全面开发的最先进QMC代码库，包括（a）用于大规模玻色子模拟的蠕虫算法和最大熵方法，提供有关动力学可解释性的信息;（B）基于波函数的变分蒙特卡罗方法，优化大量参数;以及（c）最大限度地减少对波函数依赖的声誉QMC方法。该项目还支持在致力于推进量子物质和材料理解的多元化研究小组的背景下培训学生。PI计划在哥伦布科学博物馆举办一个物理节，主题是随机数“葡萄干到PI”。“PI是带头科学思想家计划会见一个科学家，成为一个科学家，并了解其他科学家在哥伦布市学区的英尼斯小学。PI将推出一个本科教育网站，提供10分钟的简短讲座，可以搜索，并与其他远程学习方案协调。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。材料由许多电子和离子组成，它们之间的相互作用导致了新的物质状态，例如超导体和磁体，它们来自于电子的自组织，它们的运动以及它们的内在磁取向（称为自旋）。PI将研究当电子的自旋被锁定在其运动中时，新相位可能出现的可能性。 当粒子之间的相互作用足够强以支配由于它们的运动而产生的能量时，它们的动能、具有刺猬、涡旋和螺旋结构的纹理化磁相可能产生。电子在磁性织构背景中的运动导致了与电子输运相关的材料的不寻常性质。PI还将探索量子相变。这些是在绝对零度下发生的相变。据信，这些转变可具有可达到室温的显著部分的后果。 与人们熟悉的由热涨落驱动的从水到蒸汽的相变不同，量子相变是由海森堡著名的不确定性原理引起的量子涨落驱动的。 量子相变可能会导致戏剧性的变化，例如在改变粒子之间的相互作用，或施加磁场或压力时，一个量子态重新构造为完全不同的量子态。这些具有根本重要性的问题将在与包含过渡金属的氧化物材料以及被困在光晶格中的超冷原子直接相关的物理模型的背景下进行探索。该项目还支持在一个多样化的研究小组中培养学生，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一个物理节，主题是随机数“葡萄干到PI”。“PI是带头科学思想家计划会见一个科学家，成为一个科学家，并了解其他科学家在哥伦布市学区的英尼斯小学。PI将推出一个本科教育网站，提供10分钟的简短讲座，可以搜索，并与其他远程学习方案协调。

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.