Quantum Monte Carlo methods beyond the fixed-node approximation: excitonic effects and hydrogen compounds

非技术总结该奖项支持旨在为研究材料的原子和电子结构而在模拟和计算方法方面取得重大进展的研究和教育。对新型材料的理解、设计和预测涉及在量子力学水平上求解描述复杂、多粒子系统的基本量子力学定律的方程。由于主要的数学、算法和计算挑战，以及现实世界应用所需的极高精度，此类解决方案非常难以获得。此外，对新材料的研究往往涉及非常复杂的量子现象的相互作用，这为发现材料和信息处理、光学、磁性和其他应用的新功能提供了意想不到的机会。这可能会导致发现存在于材料中的电子的新量子态。拟议的研究思路建立在被称为量子蒙特卡罗的方法的以前发展的基础上，这些方法在克服涉及的许多根本挑战方面特别有希望。这一成功的战略将分析洞察力、统计抽样技术和并行体系结构计算机器的能力结合到独特而强大的工具中，使我们能够攻击量子研究领域，这些领域在几年前都是不可想象的。关键的发展涉及新的算法，这些算法使用更强大的数学框架和更高效的算法结构，显著提高了计算材料关键特性的稳健性和准确性。这些进展将应用于两组深入研究的材料：i)氢化合物，据推测，这是一种新的超导体，将在室温附近工作；ii)表现出强烈量子现象的化合物，这对光学应用以及物质新量子状态的出现是必不可少的。拟议的项目将为学生提供令人兴奋的量子物理、计算和模拟技术方面的研究、教育和培训机会，所有这些都对总体技术进步和下一代劳动力至关重要。这些研究和教育活动为有抱负的年轻科学家提供了一个激励的环境，他们来自不断增长的NCSU学生群体，这是北卡罗来纳州最大的学生群体，其中包括许多来自农村和弱势社区的学生。在分析、计算和建模技术方面获得的技能在学术界、国家实验室和各种行业的就业市场上都有很高的需求。为利用这些机会做好准备，将为未来的STEM劳动力带来具有吸引力、高薪和智力回报的职业道路。技术总结该奖项支持旨在材料原子和电子结构研究的模拟和计算方法方面取得重大进展的研究和教育。电子结构量子蒙特卡罗(QMC)方法通常用于计算基态能隙、内聚能、电子密度和其他性质，方法是用关联多体波函数高精度地显式求解定常薛定谔方程。在这个项目中，PI将扩展QMC多体波函数方法的能力，以描述激子以及具有显著电子关联的系统中的激子相关现象。为此，将探索基于轨道对的波函数，并结合涉及双分量自旋的最新进展，在涉及磁、光和集体电子态的系统中捕捉强关联。特别是，这种形式使得描述各种材料中的激子凝聚成为可能。下一个令人感兴趣的领域涉及将QMC方法应用于含有较重元素的二元氢化物化合物，如硫或Y，据推测这些化合物表现出接近室温的超导电性，特别是在高压下。然而，由于实验的挑战，现有的数据非常有限，我们对这些材料和现象的理解还远远没有得到解决。这些计划包括应用QMC方法来阐明原子和电子结构、状态方程以及质子零点运动和非谐效应在这些化合物中的作用。在基本水平上，自旋相关相互作用的最新发展使得固定节点和固定相位版本的QMC能够平滑地变化。这为增加变分自由度以及达到超过当前固定节点/相位精度限制提供了新的可能性。其目的是探索有可能将常见的固定节点/相位偏差减少近一个数量级的方向，为深入了解电子-电子关联和复杂的量子现象开辟新的途径。该奖项反映了NSF的法定使命，并通过使用基金会的智力优势和更广泛的影响审查标准进行评估，被认为值得支持。

NONTECHNICAL SUMMARYThis award supports research and education aimed to make significant advances in simulation and computational approaches for studies of atomic and electronic structures of materials. Understanding, design, and prediction of new types of materials involve solving the equations that describe fundamental quantum mechanical laws for complex, many-particle systems at the level of quantum mechanics. Such solutions are exceptionally difficult to obtain due to major mathematical, algorithmic and computational challenges as well as due to exceedingly high accuracy required for real world applications. In addition, research on new materials often involves very intricate interplays of quantum phenomena that provide unexpected opportunities to discover materials and new functionalities for information processing, optical, magnetic and host of other applications. This may lead to the discovery of new quantum states of electrons that exist in materials. The proposed research ideas build upon previous developments of methods known as quantum Monte Carlo, that are particularly promising in overcoming many of the fundamental challenges involved. This successful strategy combines analytical insights, statistical sampling techniques and the power of parallel architecture computing machines into unique and powerful tools that enable us to attack areas of quantum research that were unthinkable even a few years ago. Key developments involve new algorithms that significantly increase robustness and accuracy of calculating crucial characteristics of materials using a more powerful mathematical framework and more efficient algorithmic constructions. These developments will be applied to two intensely studied groups of materials: i) hydrogen compounds, which are putatively claimed to be new superconductors that would work close to room temperatures; ii) to compounds that exhibit strong quantum phenomena that are essential for optical applications as well as for occurrence of new quantum states of matter. Proposed projects will provide exciting research, education, and training opportunities for students in quantum physics, computational and simulation techniques, all of which are crucial for technological advances in general and for the next generation workforce. These research and education activities offer a stimulating environment for aspiring young scientists from the growing body of NCSU students, the largest in North Carolina, that includes many students from rural and disadvantaged communities. Acquired skills in analytical, computational, and modelling techniques are in high demand on job markets throughout academia, national laboratories, and a variety of industries. Preparation to take advantage of such opportunities leads to attractive, highly paid, and intellectually rewarding career paths for future STEM workforce. TECHNICAL SUMMARYThis award supports research and education aimed to make significant advances in simulation and computational approaches for studies of atomic and electronic structures of materials. Electronic structure quantum Monte Carlo (QMC) methods are routinely used to calculate fundamental gaps, cohesion energies, electronic densities, and other properties by solving the stationary Schroedinger equation with high accuracy explicitly using correlated many-body wave functions. In this project the PI will expand the ability of QMC many-body wave function methods to describe excitons and excitonic related phenomena in systems with significant electron correlations. For this purpose, pair orbital-based wave functions combined with recent developments that involve two-component spinors will be explored to capture strong correlations in systems that involve magnetic, optical, and collective electronic states. In particular, this form enables the description of exciton condensates in a variety of materials. The next area of interest involves the application of QMC methods to binary hydride compounds involving a heavier element such as sulfur or yttrium that are putatively claimed to exhibit near-room temperature superconductivity particularly at high pressures. However, due to experimental challenges the existing data is very limited and our understanding of these materials and phenomena is very far from being settled. The plans involve applications of QMC methods to elucidate atomic and electronic structures, equations of state, and the role of proton zero-point motion and anharmonic effects in these compounds. At the fundamental level, recent developments for spin-dependent interactions enable smooth variation between fixed-node and fixed-phase versions of QMC. This opens new possibilities to increase variational freedom as well as to reach beyond the current fixed node/phase accuracy limit. The intention is to explore directions that have potential to decrease the commonly encountered fixed-node/phase bias by almost an order of magnitude, opening new avenues for insights into electron-electron correlations and intricate quantum phenomena.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.