Excellence in research: quantum few-body systems in quantum materials

The National Science Foundation Office of Integrative Activities awarded Central State University $499,990 on September 1, 2026, under the Integrative Activities program (CFDA 47.083) to develop computational tools for studying quantum few-body systems in ultrathin quantum materials.

The project focuses on building a momentum-space Yakubovsky framework to investigate how charged particles interact within materials only one to several atomic layers thick. Research aims to explain particle binding mechanisms, structural stability, and how particle arrangement affects light absorption and emission, with potential applications to solar-energy devices, light-emitting technologies, sensors, and quantum information systems.

The award provides research and training for nine students at Central State University, who gain experience in high-performance computing, scientific problem-solving, data analysis, and advanced computing resources. Students work collaboratively with researchers from partner universities in Ohio and Brazil, present findings, and develop skills supporting graduate study and STEM careers. Research findings, educational materials, and computer tools will be made publicly available.

Performance occurs in Wilberforce, Ohio, with a period of performance from September 1, 2026, through August 31, 2029.

Abstract

Nontechnical summary some of today?s most promising materials are only one to several atomic layers thick, typically less than a few nanometers?tens of thousands of times thinner than a human hair. These ultrathin materials can interact with light and electricity in unusual ways, creating opportunities for future technologies in energy, communication, sensing, and computing. However, scientists still do not fully understand how the tiny, charged particles inside these materials interact with one another or how those interactions affect the material?s behavior. New computer-based tools are developed to study groups of interacting particles in ultrathin materials. The research may help explain how these particles form stable structures, how strongly they are bound together, and how their arrangement affects the way a material absorbs and emits light. The knowledge gained may contribute to the scientific foundation for future advances in solar-energy devices, light-emitting technologies, sensors, and quantum information systems. The tools developed through the project may also support investigations of related questions in other areas of physics and materials science. The project provides research and training opportunities for nine students at central state university who gain experience in high-performance computing, scientific problem-solving, data analysis, and the use of advanced computing resources. They work with researchers from partner universities in ohio and brazil, participate in collaborative research activities, present their findings, and develop skills that support graduate study and careers in science, technology, engineering, and mathematics. Research findings, educational materials, and computer tools developed through the project will be shared publicly to benefit students, educators, and researchers. Technical summary the PIS develops a momentum-space yakubovsky framework for describing biexcitons as four-particle bound states consisting of two electrons and two holes in two-dimensional semiconductor materials. The central scientific problem is the accurate numerical solution of the schr?dinger equation for four charged particles that experience attractive electron-hole interactions and repulsive electron-electron and hole-hole interactions. The consistent inclusion of these interactions, particularly the long-range repulsive contributions, presents substantial computational challenges. The research team formulates seven coupled yakubovsky integral equations representing the independent configurations of a biexciton. These equations describe both three-plus-one and two-plus-two particle arrangements and incorporate jacobi momentum coordinates, two-particle transition matrices, particle-permutation operators, and transformations among different coordinate systems. The research team also derives the fourier transformation of the biexciton wave function from momentum space to configuration space. This transformation enables calculations of particle separations, angular correlations, spatial distributions, and geometrical structures. Optimized parallel computer codes are developed and implemented in a high-performance computing environment. The resulting mathematical framework and computational codes are validated through comparison with established results for four identical particles interacting through attractive forces. The validated framework is then applied to biexcitons using the rytova-keldysh interaction, which describes screened electrical interactions in two-dimensional semiconductor materials. Extensions of the screening and extrapolation methods previously developed by the PI and collaborators for bound states of three charged particles are used to address electron-electron and hole-hole repulsions in biexcitons. The calculations determine biexciton binding energies and wave functions in momentum and configuration spaces and provide a quantitative description of biexciton geometrical structure. The research provides a theoretical and computational foundation for future investigations of bound states consisting of five charged particles interacting through both attractive and repulsive forces. 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.- subawards are not planned for this award.