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

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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.