QERNEL: A Foundation Model for Moiré Quantum Materials

A team of researchers has introduced QERNEL, a foundational neural wavefunction that variationally addresses families of parameterized many-electron Hamiltonians, effectively capturing ground states across parameter space within one model. By integrating FiLM-based parameter conditioning with efficient architectural components—such as mixture of experts and grouped-query attention—QERNEL enhances expressivity while maintaining low computational demands. The model was utilized for interacting electrons in semiconductor moiré heterobilayers, training a single weight-shared model for systems containing up to 150 electrons. By conditioning on moiré potential depth to solve the many-electron Schrödinger equation, QERNEL identifies both quantum liquid and crystal states, revealing a distinct phase transition characterized by sudden shifts in interaction energy and charge density. This research lays the groundwork for moiré quantum materials and a scalable architecture for future studies.