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

非技术性总结该职业奖支持理论研究和教育，重点是弥合量子材料的实验探针和理论理解之间的差距，量子力学的基本方面在其功能和特性中发挥着至关重要的作用。例子包括超导体，量子磁体和拓扑绝缘体，它们是通过其体积绝缘的材料，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，对技术应用至关重要。然而，模拟这些材料并预测它们的性质可能具有挑战性，并且由于它们的电子自由度之间的量子力学纠缠而需要计算。为了解决这些复杂问题，研究小组将开发和分发最先进的计算机代码，用于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：材料与特定频率的光相互作用的过程，例如，以不同的频率发射光。这些过程的特定频率和偏振依赖性可以提供有关潜在量子力学自由度及其纠缠的精确线索。研究团队将与实验小组合作，提供材料特定的理论分析，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层次的学生，包括高中暑期实习生。同时，PI与温斯顿-塞勒姆/福赛斯县学校董事会合作，开发了一个大学课程，培训学生进行科学推广和公共传播。后者是研究生涯中越来越重要的一个方面，学生很少接受正式培训。本课程旨在弥合这一差距，并提供一个框架和课程材料，可以由其他机构改编。这些PI的教育和外展活动将有助于与当地社区的接触，有助于培养下一代研究人员和教育工作者，并有助于为未来的第一代大学参与者奠定基础，以追求科学事业。技术摘要该职业奖支持理论研究和教育，以处理复杂量子材料的数值方法。研究小组将利用费米子系统矩阵乘积态方法的最新发展，实现基于第一原理的计算，能够处理大轨道空间的低能有效哈密顿量。这些多体方法自然地捕获了局部自由度的完整“纠缠结构”，从而为估计一般耦合常数提供了精确的工具，即使是最复杂的自旋轨道材料。该方法将允许计算材料特定的动态有效哈密顿量，以解决非线性响应，如二次谐波产生和四波混频。分析相关材料的实验的理论支持，目前显着落后于实验能力。这些方法将被应用于拓扑激子和新型量子自旋轨道液体的搜索，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外联和公开分发数字代码对研究和教育产生直接影响。通过与当地的第一名高中，科学家在课堂活动的伙伴关系，并开发一个新的大学水平的科学推广课程，维克森林学生在当地推广的参与将显着扩大。此外，来自低收入背景的暑期实习生将被招募参加研究和职业发展活动，与研究生导师。该奖项反映了NSF的法定使命，并已被认为是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的支持。

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.