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

职业：研究量子材料线性和非线性响应的有效哈密顿向下折叠方法

• 批准号: 2338704
• 负责人: Stephen Winter
• 金额: $ 55万
• 依托单位: Wake Forest University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2024
• 资助国家: 美国
• 起止时间: 2024-09-01 至 2029-08-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2338704&HistoricalAwards=false
• 关键词: CAREER; Effective; Hamiltonian; Downfolding; Methods

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.

非技术摘要这一职业奖支持理论研究和教育，重点是弥合实验探针与量子材料的理论理解之间的差距，量子力学的基本方面在其功能和财产中起着重要的作用。例子包括超导体，量子磁铁和拓扑绝缘子，它们正在通过其大量进行绝缘材料，但可以在其表面上进行电力。这些材料为技术应用提供了独特的电子，光学和磁性。但是，由于其电子自由度之间的量子机械纠缠，模拟这些材料并预测其性质可能是具有挑战性的，并且在计算上要求很高。为了解决这些并发症，研究团队将开发和分发最新的计算机代码，以构建特定于材料的有效模型。一个特定的焦点将是用于非线性响应的模型：材料与特定频率相互作用的过程，例如，以不同频率发出光。这些过程的特定频率和极化依赖性可以提供有关基本量子机械自由度及其纠缠程度的精确线索。研究团队将与实验组合作，提供特定于材料的理论分析，以支持和解释量子材料中的这种非线性响应。研究团队将包括各个级别的学生，包括高中暑期实习生。同时，PI与Winston-Salem/Forsyth County学校董事会合作，开发了大学级课程培训科学外展和公共交流的学生。后者是研究职业越来越重要的方面，在该职业中，学生很少接受正规培训。本课程旨在弥合这一差距，并提供其他机构可以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互动，为培训下一代研究人员和教育工作者做出贡献，并为可能成为第一代大学参与者从事科学职业的基础。技术摘要这一职业奖支持理论研究和教育，以对处理复杂的数量材料进行数值方法。研究团队将利用矩阵产品状态方法的最新发展，以使费米子系统实施基于第一原理的低能量有效汉密尔顿人的计算，能够治疗大轨道空间。这些多体方法自然捕获了局部自由度的完整“纠缠结构”，因此即使是最复杂的旋转轨道材料，也提供了估计通用耦合常数的准确工具。这些方法将允许计算特定于材料的动力学有效哈密顿量，以解决第二次谐波产生和四波混合等非线性响应。对当前相关材料进行此类实验的理论支持当前落后于实验能力。这些方法将应用于搜索拓扑激子和新型量子旋转轨道液体，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外展和数值代码的公共分布对研究和教育产生直接影响。尽管与本地标题1高中的合作伙伴关系，课堂活动中的科学家以及新的大学科学外展课程的发展，但韦克森林学生参与当地外展活动将大大扩展。此外，将招募来自低收入背景的暑期实习生参加研究和职业发展活动。该奖项反映了NSF的法定任务，并被认为是值得通过基金会的知识分子优点和更广泛影响的评估标准通过评估来获得支持的。