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

超越固定节点近似的量子蒙特卡罗方法：激子效应和氢化合物

• 批准号: 2316007
• 负责人: Lubos Mitas
• 金额: $ 34.65万
• 依托单位: North Carolina State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2023
• 资助国家: 美国
• 起止时间: 2023-09-15 至 2026-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2316007&HistoricalAwards=false
• 关键词: Quantum; Monte; Carlo; methods; beyond

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.

非技术摘要这一奖项支持研究和教育，旨在在模拟和计算方法方面取得重大进展，以研究原子和电子结构的材料结构。了解新型材料的理解，设计和预测涉及求解描述量子力学水平复杂的多粒子系统基本量子力学定律的方程。由于重大的数学，算法和计算挑战以及由于现实世界应用所需的精度非常高，因此难以获得此类解决方案。此外，对新材料的研究通常涉及量子现象的非常复杂的相互作用，这些相互作用提供了意外的机会，可以发现信息处理，光学，磁性和其他应用的新功能。这可能会导致发现材料中存在的电子的新量子状态。拟议的研究思想以先前的量子蒙特卡洛的发展为基础，这些方法在克服许多基本挑战方面尤其有希望。这种成功的策略结合了分析见解，统计抽样技术和并行体系结构计算机的功能，使我们能够攻击几年前甚至几年前都无法想象的量子研究领域。主要的发展涉及新算法，这些算法可显着提高使用更强大的数学框架和更有效的算法结构来计算材料关键特征的鲁棒性和准确性。这些发展将应用于两种经过深入研究的材料组：i）氢化合物，这些化合物被推测为新的超导体，可以接近室温； ii）对于表现出强量子现象的化合物，这对于光学应用以及新的物质量子状态至关重要。拟议的项目将为量子物理学，计算和仿真技术的学生提供令人兴奋的研究，教育和培训机会，所有这些都对一般的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学生的有抱负的年轻科学家提供了一个刺激性的环境，其中包括许多来自农村和不利社区的学生。获得分析，计算和建模技术的技能对整个学术界，国家实验室和各种行业的就业市场需求很高。准备利用此类机会的准备可以为未来的STEM劳动力带来吸引力，高薪和知识上有回报的职业道路。技术摘要奖支持研究和教育，旨在在模拟和计算方法方面取得重大进展，以研究原子和电子结构的材料结构。电子结构量子蒙特卡洛（QMC）方法通常用于计算基本间隙，内聚力能，电子密度和其他特性，通过使用相关的许多身体波函数来明确求解高精度。在该项目中，PI将扩展QMC多体波函数方法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的能力。为此，将探索涉及两组分纺纱器的最新发展的基于轨道的波函数，以捕获涉及磁性，光学和集体电子状态的系统中的强相关性。特别是，此形式可以描述各种材料中的激子凝结。感兴趣的下一个区域涉及将QMC方法应用于二元氢化物化合物，涉及较重的元素，例如硫或YTTRUM，这些元素被推测地称为近室温度超导性，尤其是在高压下。但是，由于实验挑战，现有数据非常有限，我们对这些材料和现象的理解远非解决。该计划涉及QMC方法在这些化合物中阐明原子和电子结构，状态方程以及质子零点运动和非谐作用的作用的应用。在基本层面，旋转依赖性相互作用的最新发展使QMC的固定节点和固定相版本之间的平滑变化。这为增加变分的自由以及超出当前固定节点/相准确度限制的新可能性开放了新的可能性。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，为对电子电子相关性的见解开辟了新的途径和复杂的量子现象。这奖反映了NSF的法定任务，并通过评估基础的智力效果和宽阔的范围来评估支持，并以评估值得评估。