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

该奖项旨在支持在材料原子和电子结构的模拟和计算方法研究方面取得重大进展的研究和教育。理解、设计和预测新型材料涉及在量子力学水平上解决描述复杂、多粒子系统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，这种解决方案非常难以获得。此外，对新材料的研究通常涉及非常复杂的量子现象的相互作用，为发现信息处理、光学、磁性和其他应用的材料和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。提出的研究思路建立在量子蒙特卡罗方法的先前发展基础上，该方法在克服许多涉及的基本挑战方面特别有希望。这种成功的策略将分析洞察力、统计抽样技术和并行架构计算机器的能力结合在一起，形成独特而强大的工具，使我们能够攻击几年前甚至无法想象的量子研究领域。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有效的算法结构，显着提高计算材料关键特性的鲁棒性和准确性。这些发展将应用于两组被深入研究的材料：1)氢化合物，它被认为是一种新的超导体，可以在接近室温的条件下工作；Ii)表现出强量子现象的化合物，这些现象对光学应用以及物质新量子态的出现至关重要。拟议的项目将为量子物理、计算和模拟技术方面的学生提供令人兴奋的研究、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北卡州立大学不断壮大的学生群体中有抱负的年轻科学家提供了一个鼓舞人心的环境，北卡州立大学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。在整个学术界、国家实验室和各种行业的就业市场上，获得分析、计算和建模技术的技能都有很高的需求。准备好利用这些机会，为未来的STEM劳动力带来有吸引力、高薪和智力回报的职业道路。该奖项支持旨在为材料的原子和电子结构的模拟和计算方法研究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本间隙、内聚力能、电子密度和其他性质，通过使用相关多体波函数显式高精度地求解平稳薛定谔方程。在这个项目中，PI将扩展QMC多体波函数方法的能力，以描述具有显著电子相关性的系统中的激子和激子相关现象。为此，将探索基于对轨道的波函数与涉及双组分旋量的最新发展相结合，以捕获涉及磁性，光学和集体电子态的系统中的强相关性。特别是，这种形式能够描述各种材料中的激子凝聚体。下一个令人感兴趣的领域涉及QMC方法在二元氢化物化合物中的应用，这些化合物含有较重的元素，如硫或钇，这些元素被认为在高压下表现出接近室温的超导性。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。这些计划包括应用量子力学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调和效应在这些化合物中的作用。在基本层面上，自旋依赖相互作用的最新发展使QMC的固定节点和固定相位版本之间的平滑变化成为可能。这为增加变分自由度以及超越当前固定节点/相位精度限制开辟了新的可能性。其目的是探索有可能将常见的固定节点/相位偏差减少几乎一个数量级的方向，为深入了解电子-电子相关性和复杂的量子现象开辟新的途径。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值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.