CAREER: Effective Hamiltonian Downfolding Methods for Studying Linear and Nonlinear Responses of Quantum Materials

非技术总结这个职业奖项支持理论研究和教育，专注于弥合量子材料的实验探测和理论理解之间的差距，对量子材料来说，量子力学的基本方面在其功能和性质中发挥着至关重要的作用。例子包括超导体、量子磁铁和拓扑绝缘体，它们是通过块状材料绝缘的，但可以在其表面导电。这些材料具有独特的电子、光学和磁性，对技术应用非常重要。然而，由于这些材料的电子自由度之间存在量子力学纠缠，模拟这些材料并预测它们的性能可能具有挑战性和计算要求。为了解决这些复杂性，研究小组将开发和分发最先进的计算机代码，以构建特定材料的有效模型。一个特别的焦点将是非线性响应的模型：其中材料与特定频率的光相互作用的过程，例如，以不同频率发射光。这些过程的特定频率和偏振相关性可以提供关于潜在的量子力学自由度和它们的纠缠的精确线索。研究团队将与实验小组合作，提供针对材料的理论分析，以支持和解释量子材料中的这种非线性响应。研究团队将包括不同水平的学生，包括高中暑期实习生。与此同时，国际和平协会与温斯顿-塞勒姆/福赛斯县学校董事会合作，开发了一门大学级课程，培训学生进行科学推广和公共传播。后者是研究生涯中一个越来越重要的方面，学生很少接受正式培训。本课程旨在弥补这一差距，并提供可供其他机构改编的框架和课程材料。这些PI的教育和外展活动将有助于与当地社区接触，有助于培训下一代研究人员和教育工作者，并帮助为未来的第一代大学学员追求科学事业奠定基础。TECHNICAL SUMMARY这个职业奖项支持处理复杂量子材料的数值方法的理论研究和教育。研究小组将利用费米子系统矩阵乘积状态方法的最新发展，实施基于第一原理的低能量有效哈密顿量的计算，能够处理大轨道空间。这些多体方法自然而然地捕捉到了局部自由度的完整的“纠缠结构”，从而为估计一般耦合常数提供了准确的工具，即使对于最复杂的自旋轨道材料也是如此。这些方法将允许计算特定于材料的动力学有效哈密顿量，以解决诸如二次谐波产生和四波混频等非线性响应。目前，对相关材料上的此类实验进行分析的理论支持远远落后于实验能力。这些方法将用于寻找拓扑激子和新的量子自旋轨道液体，以及对隐藏有序相的非线性响应的理解。这些活动将通过学生培训、K-12外展和公开分发数字代码对研究和教育产生直接影响。通过与当地第1标题高中、课堂活动中的科学家以及开发新的大学一级科学外联课程建立伙伴关系，维克森林的学生参与当地外联活动的范围将大大扩大。此外，来自低收入背景的暑期实习生将在研究生导师的帮助下参与研究和职业发展活动。该奖项反映了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。

NONTECHNICAL SUMMARYThis CAREER award supports theoretical research and education focused on bridging the gap between experimental probes and theoretical understanding of quantum materials, for which fundamental aspects of quantum mechanics play essential roles in their function and properties. Examples include superconductors, quantum magnets, and topological insulators which are insulating materials through their bulk but can conduct electricity on their surfaces. These materials offer unique electronic, optical, and magnetic properties important for technological applications. However, simulating these materials and predicting their properties can be challenging and computationally demanding due to the quantum mechanical entanglement between their electronic degrees of freedom. In order to address these complications, the research team will develop and distribute state-of-the-art computer codes for constructing material-specific effective models. A particular focus will be models for non-linear responses: processes in which the materials interact with light of a particular frequency, and, for example, emit light at a different frequency. The particular frequency and polarization dependence of these processes can provide precise clues about the underlying quantum mechanical degrees of freedom and their entanglement. The research team will work in collaboration with experimental groups to provide material-specific theoretical analysis to support and interpret such non-linear responses in quantum materials.The research team will include students at various levels, including high school summer interns. Concurrently, the PI has partnered with the Winston-Salem/Forsyth County school board to develop a university level course training students in scientific outreach and public communication. The latter is an increasingly vital aspect of a research career, in which students rarely receive formal training. This course aims to bridge this gap and provide a framework and course materials that can be adapted by other institutions. These PI's education and outreach activities will serve to engage with local community, contribute to training the next generation of researchers and educators, and help build a foundation for would-be first-generation university attendees to pursue scientific careers.TECHNICAL SUMMARYThis CAREER award supports theoretical research and education towards numerical methods for treating complex quantum materials. The research team will leverage recent developments in Matrix Product State approaches for fermionic systems to implement first-principles based calculation of low-energy effective Hamiltonians capable of treating large orbital spaces. These many-body approaches naturally capture the full "entanglement structure" of local degrees of freedom, and thus provide accurate tools for estimating generic coupling constants, even for the most complicated spin-orbital materials. The methods will allow for the calculation of material-specific dynamical effective Hamiltonians, to address nonlinear responses such as second harmonic generation and four-wave mixing. Theoretical support for analyzing such experiments on correlated materials currently lags significantly behind experimental capabilities. The methods will be applied to the search for topological excitons and novel quantum spin-orbital liquids, and the understanding of nonlinear responses of hidden ordered phases. These activities will have direct impact on research and education through student training, K-12 outreach, and public distribution of numerical codes. Though partnerships with local Title 1 high-schools, Scientist in the Classroom events, and the development of a new university-level Scientific Outreach course, the participation of Wake Forest students in local outreach will be significantly expanded. In addition, summer interns from low-income backgrounds will be recruited to participate, with graduate student mentors, in research and career-development activities.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.