LEAPS-MPS: Correlated Methods for Correlated Phases

About This Grant

NON-TECHNICAL SUMMARY A deep understanding of how electrons behave in materials has powered some of the most transformative technologies of modern life, from personal computing and mobile devices to weather prediction and artificial intelligence. These advances were made possible through breakthroughs in semiconductor technology, for example the invention of the transistor. Today, researchers are exploring a new class of semiconductor interfaces, known as two-dimensional "moiré materials", that may drive the next generation of innovations. These materials have the potential to support new technologies such as ultra-efficient spintronic devices and may one day become the building blocks of fault-tolerant quantum computers. However, scientific understanding of these materials is still in its early stages. In particular, existing theoretical models often rely on simplified, qualitative approaches that cannot fully capture the complex behaviors observed in experiments. This project aims to develop more accurate, predictive tools to model these systems by combining machine learning (ML) techniques with advanced quantum simulation methods. The goal is to discover new electronic phases of matter, characterize their properties, and generate reliable benchmark data to support future research. In addition to advancing materials science, the project will broaden access to computational research. The principal investigator (PI) will mentor undergraduate students in areas such as programming, scientific computing, and data analysis. The project will also make use of Hofstra University’s new high-performance computing cluster and include outreach events designed to introduce students from across disciplines to essential computational research skills. TECHNICAL SUMMARY This project investigates strongly correlated electronic phases in two-dimensional moiré materials, with the goal of advancing our theoretical understanding of these materials from qualitative to quantitative. Moiré materials host long-range periodic potentials that enhance electron-electron interactions, leading to unconventional electronic and magnetic states such as generalized Wigner crystals, superconductors, and topological insulators. These phenomena are not well described by standard mean-field theory. The intellectual merit of the project lies in its use of many-body wavefunction techniques, which can uncover novel correlated electronic phases that are inaccessible to the standard approach. The research that will be carried out will employ a multi-messenger computational framework that integrates density functional theory, diffusion Monte Carlo, and neural quantum states simulations. The PI will use machine learning techniques to expand the flexibility of variational ansätze for strongly correlated systems and interpret the emergent solutions through the lens of many-body physics. High-accuracy diffusion Monte Carlo simulations can help distinguish physically meaningful phases from artifacts of variational overfitting. The resulting benchmark datasets will serve as reference points for evaluating and improving approximate methods. The broader impacts of the funded activities will include: (1) establishing a computational research community at Hofstra University and neighboring institutions, including Adelphi University and Nassau Community College. The PI will host tutorials to teach the basics of ML and computational research to interested students, introducing skills that are transferable across disciplines; (2) training undergraduate researchers in high-performance computing, AI-assisted simulation, and scientific software development; and (3) using the project’s outputs to enhance interdisciplinary education in computational science. By leveraging Hofstra’s new high-performance computing infrastructure and its connections with the local community, this project will contribute to the development of a more inclusive and data-literate scientific workforce prepared for the 21st-century. STATEMENT OF MERIT REVIEW 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.