AI 中文总结
针对强关联量子材料模拟中FNQS的精度与采样成本问题，提出FNEH，可准确恢复相边界、降低计算成本，在莫尔材料中验证了其有效性。
AI 中文摘要
模拟强关联量子材料通常涉及的不是单个哈密顿量，而是一族哈密顿量，其基态会随实验可调耦合参数演化。基础神经网络量子态（FNQS）为跨这类族的多体计算提供了一种有前景的途径，但在相变附近会失去精度，且仍会产生随目标耦合数量增长的不可忽略的采样成本。我们提出了基础神经网络有效哈密顿量（FNEH），它将哈密顿量族投影到由在选定耦合下采样的FNQS张成的紧致子空间上。通过变分组合参数空间中的FNQS，FNEH系统地改进了它们的基态近似，并能恢复基础模型误判的相边界。一旦采样得到所需的算子矩阵元，FNEH就可以在耦合、可观测量和相边界上进行扫描，其成本由小型有效哈密顿量的维度决定，无需在每个目标耦合处重复进行神经网络采样。我们在强关联莫尔材料中验证了FNEH，它能准确分辨竞争相，实现高分辨率多维相扫描，并大幅降低探索多个目标哈密顿量的计算成本。这些结果为用基础模型研究强关联量子材料开辟了新途径。
英文摘要
Simulating strongly correlated quantum materials often involves not a single Hamiltonian, but a family of Hamiltonians whose ground states evolve across experimentally tunable couplings. Foundation neural quantum states (FNQS) offer a promising route to amortizing many-body calculations across such families, but can lose accuracy near phase transitions and still incur non-negligible sampling costs that grow with the number of target couplings. We introduce the Foundation Neural Effective Hamiltonian (FNEH), which projects a Hamiltonian family onto a compact subspace spanned by FNQS sampled at selected couplings. By variationally combining FNQS across parameter space, FNEH systematically improves their ground-state approximation and can recover phase boundaries that the foundation model misidentifies. Once the required operator matrix elements are sampled, FNEH enables sweeps over couplings, observables, and phase boundaries at a cost governed by the small effective-Hamiltonian dimension, without repeated neural-network sampling at every target coupling. We demonstrate FNEH in strongly correlated moiré materials, where it accurately resolves competing phases, enables high-resolution multidimensional phase scans, and substantially reduces the computational cost of exploring many target Hamiltonians. The results open a new avenue for studying strongly correlated quantum materials with foundation models.
