Simulation Studies of Ground State Phases and Criticality in Correlated Quantum Matter

非技术性总结该奖项支持理论研究和教育开发方法和算法的模拟材料中的电子状态。 材料的特性来自于它们的微观结构：原子和分子。在典型的金属中，一部分电子与单个原子分离并在系统中迁移，而在其他材料中，所有电子保持局部化。在这两种情况下，电子都赋予了材料在电子和其他技术应用中所利用的电和磁特性。该项目旨在增加我们对电子由于相互作用而形成丰富的不同复杂状态的方式的理解。相互作用本质上是电磁的，并且取决于电子嵌入的环境，即特定的材料及其外部条件。就像水可以以三种不同的公共相（液体，气体和固体）出现一样，电子也可以通过改变它们的环境，例如通过施加压力或外部磁场，在具有完全不同性质的状态之间转换。作为微观粒子，电子的运动和相互作用受量子力学控制，构建易于处理的理论模型来描述它们，并理解和利用它们的不同相位和属性，在技术上极具挑战性。在这个项目中，通过大规模的计算机模拟研究了一组与局域电子材料相关的模型。电子自旋（磁矩）在不同模式中的排列取决于它们如何相互作用。该项目的核心是了解具有有序自旋模式的状态如何“熔化”，即进入无序状态，或进入另一种类型的有序状态。基础知识的进步对于实现进一步的基础进步和应用非常重要。除了科学目标之外，该项目还包括培养研究生最先进的建模和计算机模拟，并通过应用开发的方法和模型为其他研究人员创建用户友好的软件。PI还通过继续参与暑期学校和类似的教育活动，参与更广泛的培训活动。技术概述该奖项支持理论研究和教育，开发材料中电子态模拟的方法和算法。晶格量子磁体在量子多体物理中发挥着重要作用，并为研究经典统计力学之外的集体行为提供了许多机会。在这个项目中，最低限度的晶格模型被用来捕捉实验和理论相关的普遍现象，无偏的数值工具，以获得结论性的结果，基态，激发和临界缩放的一般属性。在缺乏严格的解析解的情况下，这种数值精确的结果是我们理解量子材料的基石。一组相互关联的调查，提出了解决一些最有趣的方面的量子相变超越传统的朗道-金兹伯格-威尔逊范式。我们将对几个晶格模型进行无偏数值模拟，在这些模型中，当接近量子临界点时，第二个长度尺度出现在传统的关联长度旁边。在以前工作的基础上，我们将在PI以前提出的J-Q模型类中进一步检验在AFM-VBS转变处涉及两个同时发散的长度尺度的标度假设，其目的是牢固地建立以有限尺寸和有限温度标度形式出现的指数之间的所提出的关系。此外，一类新的量子时钟模型被提出作为一个潜在的更简单的系统，在其中调查和理解的起源异常的两个长度标度。对J-Q模型也将进行更详细的研究，包括研究临界点和两个有序相的无序效应。为了促进QMC动态特性的研究，将开展随机解析延拓方法的工作，该方法显示出比迄今为止使用的其他解析延拓方法更好的频率分辨率。除了其科学目标外，该项目还包括培训研究生进行最先进的建模和计算机模拟，并通过应用开发的方法和模型为其他研究人员创建用户友好的软件。PI还通过继续参与暑期学校和类似的教育活动，参与更广泛的培训活动。

NONTECHNICAL SUMMARYThis award supports theoretical research and education on developing methods and algorithms for the simulation of electronic states in materials. Materials derive their properties from their microscopic building blocks: atoms and molecules. In typical metals, a fraction of the electrons disassociate from individual atoms and migrate through the system, while in other materials all electrons remain localized. In either case, the electrons give materials the electric and magnetic properties that are exploited in electronics and other technological applications. This project aims at increasing our understanding of the ways in which electrons can form a wealth of different complex states due to their interactions with each other. The interactions are electromagnetic in nature, and depend on the environment in which the electrons are embedded, i.e. the specific material and its external conditions. In the same way as water can appear in three different common phases (liquid, gas, and solid), electrons can also transition between states with completely different properties by changing their environment, e.g. by applying pressure or an external magnetic field. Being microscopic particles, the motion and interactions of electrons are governed by quantum mechanics, and it is technically extremely challenging to construct tractable theoretical models to describe them, and to understand and exploit their different phases and properties. In this project, a set of models relevant to materials with localized electrons are studied via large-scale computer simulations. The arrangement of the spins (magnetic moments) of the electrons in different patterns is determined by how they interact with each other. At the heart of the project is understanding the way a state having a pattern of ordered spins can "melt", i.e. go into a disordered state, or go into another type of ordered state. Progress in fundamental understanding is important for achieving further fundamental advances as well as applications.In addition to its scientific goals, the project involves training graduate students in state-of-the-art modeling and computer simulations, and creating user-friendly software for other researchers by applying the methods and models developed. The PI is also involved in broader training activities, through continued involvement in summer schools and similar educational events.TECHNICAL SUMMARYThis award supports theoretical research and education on developing methods and algorithms for the simulation of electronic states in materials.Lattice quantum magnets play an important role in quantum many-body physics, and offer many opportunities for studying collective behavior beyond classical statistical mechanics. In this project, minimalistic lattice models are used to capture universal phenomena of experimental and theoretical relevance, and unbiased numerical tools are employed to obtain conclusive results for generic properties of ground states, excitations, and critical scaling. In the absence of rigorous analytical solutions, such numerically exact results are invaluable as cornerstones of our understanding of quantum materials. An interrelated set of investigations are proposed to address some of the most intriguing aspects of quantum phase transitions beyond the conventional Landau-Ginzburg-Wilson paradigm. Unbiased numerical simulations will be carried out on several lattice models in which a second length scale appears alongside the conventional correlation length upon approaching a quantum critical point.Building on previous work, a scaling hypothesis involving two simultaneously divergent length scales at the AFM-VBS transition will be further tested within the class of J-Q models proposed previously by the PI, with the goal of firmly establishing the proposed relationships between exponents appearing in finite-size and finite-temperature scaling forms. Moreover, a new class of quantum clock models are proposed as a potentially simpler class of systems in which to investigate and understand the origin of the anomalous two-length scaling. More detailed studies of J-Q models will also be carried out, including studying the effects of disorder at the critical point and in the two ordered phases. In order to facilitate QMC studies of dynamic properties, work will be carried out on a stochastic analytic continuation method, which shows promise towards delivering better frequency resolution than other analytic continuation methods used so far.In addition to its scientific goals, the project involves training graduate students in state-of-the-art modeling and computer simulations, and creating user-friendly software for other researchers by applying the methods and models developed. The PI is also involved in broader training activities, through continued involvement in summer schools and similar educational events.