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

该奖项支持旨在为材料的原子和电子结构研究在模拟和计算方法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求解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由于真实的世界应用所需的极高精度，这样的解决方案非常难以获得。此外，对新材料的研究往往涉及量子现象的非常复杂的相互作用，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量子蒙特卡罗方法的先前发展基础上，这些方法在克服所涉及的许多基本挑战方面特别有前途。这一成功的策略将分析洞察力、统计采样技术和并行架构计算机器的强大功能结合成独特而强大的工具，使我们能够攻击几年前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构造，显着提高了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深入研究的材料：i）氢化合物，据称是在接近室温下工作的新超导体; ii）表现出强量子现象的化合物，这些现象对于光学应用以及物质的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来自北卡罗来纳州最大的NCSU学生群体的有抱负的年轻科学家提供了一个激励的环境，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整个学术界，国家实验室和各种行业的就业市场上需求量很大。准备利用这些机会，为未来的STEM劳动力提供有吸引力，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研究在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本带隙、凝聚能、电子密度和其他性质，通过使用相关多体波函数以高精度显式求解定态薛定谔方程。在这个项目中，PI将扩展QMC多体波函数方法的能力，以描述具有显着电子相关性的系统中的激子和激子相关现象。为此目的，对轨道为基础的波函数结合最近的发展，涉及两个组件旋量将探索捕捉强相关性的系统，涉及磁，光，集体电子状态。特别是，这种形式使得在各种材料中的激子凝聚体的描述。下一个感兴趣的领域涉及QMC方法的应用，以二元氢化物化合物，涉及一个较重的元素，如硫或钇，被puancorously声称表现出近室温的超导性，特别是在高压下。然而，由于实验的挑战，现有的数据是非常有限的，我们对这些材料和现象的理解是非常遥远的被解决。这些计划涉及QMC方法的应用，以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/相位精度极限开辟了新的可能性。其目的是探索有可能将常见的固定节点/相位偏差降低近一个数量级的方向，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NSF的法定使命，并被认为值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估来支持。

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.