QERNEL: A Scalable Large Electron Model for Quantum Materials Discovery

The introduction of QERNEL, a scalable large electron model, marks a pivotal advancement in computational materials science, particularly for the study of strongly correlated electron systems. This foundational neural wavefunction offers a novel approach to variationally solving families of parameterized many-electron Hamiltonians, capable of capturing ground states across vast parameter spaces within a single model. By integrating FiLM-based parameter conditioning with scale-efficient architectural elements like mixture of experts and grouped-query attention, QERNEL significantly enhances expressivity while maintaining low computational cost, addressing a long-standing challenge in quantum many-body physics.

The efficacy of QERNEL is demonstrated through its application to interacting electrons in semiconductor moiré heterobilayers. A single weight-shared model was successfully trained for systems comprising up to 150 electrons, a scale previously difficult to achieve with high accuracy. By solving the many-electron Schrödinger equation conditioned on moiré potential depth, QERNEL not only accurately captures both quantum liquid and crystal states but also precisely identifies the sharp phase transition between them, characterized by abrupt changes in interaction energy and charge density. This capability is critical for understanding and engineering the exotic properties of these materials, which hold promise for next-generation electronics and quantum computing.

This work establishes a robust foundation model for moiré quantum materials and represents a significant step towards realizing a "Large Electron Model" for solids. The implications are far-reaching, potentially accelerating the discovery and design of novel materials with tailored electronic, magnetic, and superconducting properties. By providing a scalable and accurate tool for exploring complex quantum phenomena, QERNEL could unlock new frontiers in condensed matter physics and materials engineering, moving beyond empirical discovery to predictive design, thereby impacting fields from energy storage to quantum information science.