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

相关量子物质的基态相和临界性的模拟研究

基本信息

批准号：
1710170
负责人：
Anders Sandvik
金额：
$ 42.6万
依托单位：
Trustees of Boston University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-09-01 至 2020-08-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1710170&HistoricalAwards=false
关键词：
Simulation Studies Ground State Phases

项目摘要

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.

非技术摘要该奖项支持开发材料电子态模拟方法和算法的理论研究和教育。材料的特性源自其微观构件：原子和分子。在典型的金属中，一小部分电子与单个原子分离并迁移通过系统，而在其他材料中，所有电子都保持局域化。无论哪种情况，电子都会赋予材料在电子和其他技术应用中利用的电和磁特性。该项目旨在加深我们对电子由于彼此相互作用而形成丰富的不同复杂状态的方式的理解。这种相互作用本质上是电磁相互作用，并且取决于电子嵌入的环境，即特定材料及其外部条件。就像水可以以三种不同的常见相（液体、气体和固体）出现一样，电子也可以通过改变其环境在具有完全不同属性的状态之间转变，例如通过施加压力或外部磁场。作为微观粒子，电子的运动和相互作用受到量子力学的控制，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和性质在技术上极具挑战性。在该项目中，通过大规模计算机模拟研究了一组与局域电子材料相关的模型。不同模式的电子自旋（磁矩）的排列取决于它们如何相互作用。该项目的核心是理解具有有序自旋模式的状态如何“融化”，即进入无序状态，或进入另一种类型的有序状态。基础理解的进步对于实现进一步的基础进步和应用非常重要。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 还通过持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。技术摘要该奖项支持开发材料中电子态模拟方法和算法的理论研究和教育。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。在该项目中，使用简约晶格模型来捕获实验和理论相关性的普遍现象，并使用无偏数值工具来获得基态、激发和临界标度的一般性质的结论性结果。在缺乏严格的分析解决方案的情况下，这种数值精确的结果作为我们理解量子材料的基石是无价的。提出了一组相互关联的研究，以解决传统朗道-金兹堡-威尔逊范式之外的量子相变的一些最有趣的方面。将在几个晶格模型上进行无偏数值模拟，其中在接近量子临界点时，第二个长度尺度与常规相关长度一起出现。在之前的工作基础上，将在 PI 先前提出的 J-Q 模型类别中进一步测试涉及 AFM-VBS 转变处两个同时发散的长度尺度的尺度假设，其目标是牢固地建立指数之间的拟议关系以有限尺寸和有限温度缩放形式出现。此外，提出了一类新的量子时钟模型，作为一类可能更简单的系统，用于研究和理解异常两长度缩放的起源。还将对 J-Q 模型进行更详细的研究，包括研究无序在临界点和两个有序阶段的影响。为了促进动态特性的 QMC 研究，将开展随机解析连续方法的工作，该方法有望提供比迄今为止使用的其他解析连续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，并通过应用所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 还通过持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。

项目成果

期刊论文数量（24）

专著数量（0）

科研奖励数量（0）

会议论文数量（0）

专利数量（0）

Dynamic scaling of topological ordering in classical systems

DOI：
10.1103/physrevb.97.024432
发表时间：
2017-11
期刊：
Physical Review B
影响因子：
3.7
作者：
Na Xu;C. Castelnovo;R. Melko;C. Chamon;A. Sandvik
通讯作者：
Na Xu;C. Castelnovo;R. Melko;C. Chamon;A. Sandvik

The AKLT Model on a Hexagonal Chain is Gapped

六角链上的 AKLT 模型有间隙

DOI：
10.1007/s10955-019-02410-4
发表时间：
2019
期刊：
Journal of Statistical Physics
影响因子：
1.6
作者：
Lemm, Marius;Sandvik, Anders W.;Yang, Sibin
通讯作者：
Yang, Sibin

Temperature dependence of the $(\pi,0)$ anomaly in the excitation spectrum of the 2D quantum Heisenberg antiferromagnet

二维量子海森堡反铁磁体激发光谱中 $(pi,0)$ 异常的温度依赖性

DOI：
10.1088/1361-648x/ab757a
发表时间：
2020
期刊：
Journal of Physics: Condensed Matter
影响因子：
0
作者：
Wan, W;Christensen, N B;Sandvik, A W;Tregenna-Piggott, P;Nilsen, G J;Mourigal, M;Perring, T G;Frost, C D;McMorrow, D F;Rønnow, H M
通讯作者：
Rønnow, H M

Extreme Suppression of Antiferromagnetic Order and Critical Scaling in a Two-Dimensional Random Quantum Magnet

二维随机量子磁体中反铁磁序的极端抑制和临界缩放，