一个可扩展的电子模型，能统一求解多种电子系统基态。
QERNEL: a Scalable Large Electron Model
- 用条件控制+高效架构，单模型处理多参数电子系统。
- 成功模拟150个电子，捕捉到量子液体与晶体相变过程。
- 适合研究莫尔量子材料的科研人员，具强泛化能力。
我们提出QERNEL，一种基础性神经波函数，可变分求解一族参数化多电子哈密顿量，并在单一模型中捕捉其在整个参数空间内的基态。QERNEL结合基于FiLM的参数条件化与高效率架构（专家混合与分组查询注意力），在极低计算成本下显著提升表达能力。我们将QERNEL应用于半导体莫尔异质双层中的相互作用电子系统，训练出一个共享权重的模型，可处理最多150个电子的体系。通过在莫尔势阱深度条件下求解多体薛定谔方程，QERNEL成功捕捉量子液体与晶体态，并揭示两者间尖锐相变——表现为相互作用能与电荷密度的突变。本工作为莫尔量子材料建立了基础模型，并推动了面向固体的大型电子模型的发展。
原文摘要 · Abstract (English)
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.
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