QERNEL: a Scalable Large Electron Model

2026-04-28

AI Summary

This work addresses the challenge of efficiently and uniformly modeling ground-state wave functions of multi-electron systems across a parameterized Hamiltonian space by introducing a foundational neural wave function model that variationally solves for the ground states of an entire Hamiltonian family. For the first time, a single weight-shared architecture is employed to encompass moiré heterostructures with up to 150 electrons. By integrating efficient components—including FiLM-based parameter conditioning, Mixture-of-Experts (MoE), and Grouped-Query Attention (GQA)—the model successfully captures the ground-state phase diagram under deep modulation of the moiré potential, accurately resolving abrupt changes in interaction energy and charge density. This enables the identification of phase transitions between quantum liquids and crystals, demonstrating the model’s high expressivity and generalization capability in strongly correlated systems.

Abstract

We introduce QERNEL, a foundational neural wavefunction that variationally solves families of parameterized many-electron Hamiltonians and captures their ground states throughout parameter space within a single model. QERNEL combines FiLM-based parameter conditioning with scale-efficient architectural elements -- mixture of experts and grouped-query attention, substantially improving expressivity at low computational cost. We apply QERNEL to interacting electrons in semiconductor moiré heterobilayers, training a single weight-shared model for systems of up to 150 electrons. By solving the many-electron Schrödinger equation conditioned on moiré potential depth, QERNEL captures both quantum liquid and crystal states and discovers the sharp phase transition between them, marked by abrupt changes in interaction energy and charge density. Our work establishes a foundation model for moiré quantum materials and a scalable architecture toward a Large Electron Model for solids.

Problem

• many-electron problem
• moiré heterobilayers
• quantum phase transition
• ground state
• scalable model

Innovation

• QERNEL
• neural wavefunction
• mixture of experts
• grouped-query attention
• moiré quantum materials