CDS&E: Numerical Investigation of Two-Particle Response Functions of Correlated Materials

该奖项支持理论和计算研究，旨在理解强电子相关效应重要的材料的实验测量和数值模拟之间的关系。特别是，该团队将专注于获得模拟超导和磁性材料对外部应用场响应的计算数据。材料由排列在晶格中的电子和离子组成。在某些材料中，一个电子的运动与许多其他电子的运动密切相关。因此，这些材料可能表现出不寻常的行为，包括超导性、磁性或电荷顺序。这种不寻常的行为通常可以用测量材料对外部应用场响应的实验探针来研究。我们描述这种反应的标准分析工具是不够的，因此需要数值方法。该项目的主题是开发和应用精确和可控的数值方法，可以描述这些材料及其对应用领域的响应，并计算实验测量的数量。该项目将通过支持可持续开源社区软件库的开发和维护，产生更广泛的影响，这将加速未来代码的开发，并为科学界提供可靠和最先进的应用程序。目前由PI维护的软件库是少数已建立的用于强相关系统计算的开源库之一。作为该项目的一部分，研究生将接受现代理论技术和科学软件开发方面的培训。本项目旨在了解实验测量的两粒子响应函数与有效低能晶格模型的广义磁化率之间的关系，在这些系统中，强电子相关性是重要的，特别是在超导或磁性秩序已经建立的系统中。该项目将结合新开发的数值方法和大规模计算来计算紧急波动，以及在超导、电荷有序和磁性系统中测量的响应函数。磁化率揭示了系统集体激励的重要信息，在实验中可以直接测量。然而，用双粒子探针测量的广义磁化率的强相关物理，如中子散射，在理论上还没有得到很好的理解，特别是在有序相中。本项目将分析费米子晶格模型系统超导相内外的两粒子相关函数。通过为费米子晶格模型的敏感性提供可靠的结果，并通过计算响应函数，这项工作将有助于将真正的电子相关物理从依赖于模型的工件中分离出来，这反过来将有助于解释实验。相关电子材料在信息技术、能源技术、材料科学、纳米科学等现代技术应用中是必不可少的。通过澄清磁化率的基本行为及其与实验工作的关系，本项目将有助于我们对相关材料及其表征的理解。该项目将通过支持可持续开源社区软件库的开发和维护，产生更广泛的影响，这将加速未来代码的开发，并为科学界提供可靠和最先进的应用程序。目前由PI维护的软件库是少数已建立的用于强相关系统计算的开源库之一。作为该项目的一部分，研究生将接受现代理论技术和科学软件开发方面的培训。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 theoretical and computational research aimed at understanding the relationship between experimental measurements and numerical simulations of materials in which strong electronic correlation effects are important. In particular, the team will focus on obtaining computational data simulating the response to externally applied fields in superconducting and magnetic materials.Materials consist of electrons and ions arranged in a crystal lattice. In some materials, the motion of an electron is strongly interdependent on, or correlated with, the motion of many other electrons. As a consequence, these materials may exhibit unusual behavior including superconductivity, magnetism, or charge order. This unusual behavior can often be investigated with experimental probes that measure the response of a material to externally applied fields. Our standard analytical tools for describing this response are inadequate, and numerical methods are therefore needed. The subject of this project is the development and application of accurate and controlled numerical methods that can describe these materials and their response to applied fields, and compute experimentally measured quantities.The project will contribute to broader impacts by supporting the development and maintenance of sustainable open-source community software libraries, which will accelerate the development of future codes as well as provide reliable and state-of-the-art applications to the science community. The software libraries currently maintained by the PI are among the few established open-source libraries for calculations on strongly correlated systems. As part of the project, graduate students will be trained in modern theoretical techniques and in scientific software development.TECHNICAL SUMMARYThis project is aimed at understanding the relation between experimentally measured two-particle response functions and generalized susceptibilities of effective low-energy lattice models in systems where strong electronic correlations are important, and in particular systems where superconducting or magnetic order has been established. The project will combine newly developed numerical methods with large-scale calculations to compute emergent fluctuations, as well as the response functions measured in superconducting, charge ordered, and magnetic systems.Susceptibilities reveal important information about collective excitations of a system and are directly measurable in experiment. However, the strong correlation physics of generalized susceptibilities measured by two-particle probes such as neutron scattering is theoretically not well understood, especially in ordered phases. This project will analyze two-particle correlation functions in fermion lattice model systems inside and outside the superconducting phase. By providing reliable results for the susceptibilities of fermionic lattice models and by computing response functions, this work will facilitate the separation of true electron correlation physics from model-dependent artifacts, which in turn will aid in the interpretation of experiments.Correlated electron materials are essential for modern technological applications such as information technology, energy technology, materials science, and nanoscience. By clarifying the basic behavior of susceptibilities and their relation to experimental work, this project will contribute to our understanding of correlated materials and their characterization.The project will contribute to broader impacts by supporting the development and maintenance of sustainable open-source community software libraries, which will accelerate the development of future codes as well as provide reliable and state-of-the-art applications to the science community. The software libraries currently maintained by the PI are among the few established open-source libraries for calculations on strongly correlated systems. As part of the project, graduate students will be trained in modern theoretical techniques and scientific software development.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.