CAREER: Many-body expansions for strongly correlated systems

弗吉尼亚理工大学的尼古拉斯·梅霍尔得到了化学部化学理论、模型和计算方法计划的一项奖励的支持，该计划旨在开发新的理论模型和计算机软件，能够模拟所谓的“强关联”分子，这些分子已经很难用传统的量子力学模拟方法进行研究。这些类型的分子构成了一类非常重要的系统，因为它们在许多重要过程中发挥作用，如光合作用和均相过渡金属催化。强关联系统很难建模，部分原因是无法将分子分成几个小部分(“不可分离性”)，一次只关注一个部分。这需要在整个系统上进行模拟，这通常对世界上最快的超级计算机来说也太复杂了。梅霍尔教授的研究重点是研究这种不可分离性在不同类型的分子系统中的程度。然后，这些知识将被用来设计更好的理论和软件，这些理论和软件从“分离”的初始描述开始，以缓慢和可控的方式重新引入不可分离的影响，以避免计算复杂性的大幅增长，同时保持准确的结果。这项工作有可能对涉及能源生产和化学催化的技术做出贡献。梅霍尔教授的外展计划包括开发两套针对不同人口统计数据的教育模块。第一个重点是区域拘留设施中的囚犯，第二个是针对对STEM领域感兴趣的女高中生。后一项工作是与弗吉尼亚理工大学的现有活动合作完成的。该项目的主要目标有两个，1)更好地了解不可分系统，如分子聚集体和材料中的强关联分子和集体激发态，2)开发新的计算方法，能够以一种利用近似可分割性的方式对这些系统进行建模，以获得能够有效并行化在大规模计算资源上运行的计算算法。为了实现这些目标，梅霍尔教授的研究小组正在寻求两种截然不同的方法。第一种方法建立在PI的最新工作基础上，其中近似张量分解被用来模拟强关联系统中的基态和激发态。第二种方法借鉴了基于量子嵌入理论的最新领域工作，直接适用于大规模并行。这一奖项反映了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。

Nicholas Mayhall, of Virginia Tech, is supported by an award from the Chemical Theory, Models, and Computational Methods program in the Division of Chemistry to develop new theoretical models and computer software capable of simulating, so-called "strongly correlated' molecules, which have been difficult to study with conventional quantum mechanical simulation approaches. These types of molecules constitute a highly important class of systems due to their role in a number of important processes, such as photosynthesis and homogeneous transition-metal catalysis. Strongly correlated systems are difficult to model, in part, due to the inability to divide up the molecule into small parts ("inseparability") to focus on only one part at a time. This requires simulations to be performed on an entire system, which is usually far too complicated for even the world's fastest supercomputers. Prof. Mayhall's research is focused on studying the extent of this inseparability in different types of molecular systems. This knowledge will then be used to design better theories and software which start from a "separated" initial description, reintroducing the effects of inseparability in a slow and controlled manner, to avoid the large growth in computational complexity while maintaining accurate results. This work has the potential to contribute to technologies involving energy production and chemical catalysis. Prof. Mayhall's outreach program involves developing two sets of educational modules targeting distinct demographics. The first is focused on inmates in regional detention facilities, and the second is directed toward female high-school students interested in STEM fields. The latter work is done in collaboration with established activities at Virginia Tech.The main goals of this project are two-fold, 1) obtain better understanding of inseparable systems, such as strongly-correlated molecules and collective excited states in molecular aggregates and materials, and 2) develop new computational methods capable of modeling these systems in a way which exploits approximate separability to obtain computational algorithms which can be effectively parallelized to run on large scale computing resources. To achieve these goals, Prof. Mayhall's research group is pursuing two distinct approaches. The first approach builds on recent work from the PI in which an approximate tensor decomposition is used to model ground and excited states in strongly correlated systems. The second approach draws on recent work in the field based on quantum embedding theories, with direct applicability to large scale parallelization.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.