解释了密度泛函理论中能带过宽的根源，并给出修正方法。
Kohn-Sham Hamiltonian from Effective Field Theory: Quasiparticle Band Narrowing from Frozen Core Dynamics
- 基于有效场论，揭示核心动态导致能带窄化
- 修正后能带与角分辨光电子谱一致，误差仅20-35%
- 适合研究金属电子结构及第一性原理智能科学
Kohn-Sham (KS) 本征值常用于与角分辨光电子谱（ARPES）比较，并作为多体方法输入，但密度泛函理论（DFT）并未赋予其物理意义。对于碱金属和碱土金属，KS 能带宽度比 ARPES 测量值高 20-35%，这一偏差在所有交换关联泛函下均存在。我们构建了非均匀电子气的有效场论（EFT），并证明两个条件可使 KS 能带等同于准粒子能带：核心激发能量与价带费米能之间存在尺度分离，且均匀电子气近似满足伽利略不变性（经图解蒙特卡洛验证）。该结果引入一个冻结核心重整化因子 zcore，反映传统赝势忽略的动态核心激发，静态势无法捕捉。修正项 1−zcore 在碱金属中达 20-35%，但在 Al 和 Si 中低于 5%，解释了 KS 能带理论的成功与失败。我们推导出闭式后自洽公式，对 Li、Na、K、Ca、Mg、Al、Si 验证有效；预测的准粒子能带解决了长期存在的 ARPES 能带偏差问题，计算成本极低，与嵌入动力学平均场理论结果一致。本工作还示范了第一性原理代理科学，即由大模型协同推导、可控近似、符号验证与少量实验对照，形成可确定性扩展的智能范式，同时解决大模型审计瓶颈与拟合型人工智能的不可证伪性问题。
原文摘要 · Abstract (English)
Kohn-Sham (KS) eigenvalues are routinely compared with angle-resolved photoemission (ARPES) and used as input for many-body methods, yet density functional theory (DFT) assigns them no physical meaning. For alkali and alkaline-earth metals, KS bandwidths overestimate ARPES measurements by 20-35%, a discrepancy that persists across all exchange-correlation functionals. We construct an effective field theory (EFT) of the inhomogeneous electron gas and show that two conditions imply KS bands are the quasiparticle bands, up to a frozen-core renormalization factor zcore: a scale separation between core excitation energies and the valence Fermi energy, and an approximate Galilean invariance of the uniform electron gas confirmed by diagrammatic Monte Carlo. This factor reflects dynamical core excitations that conventional pseudopotentials freeze out and no static potential can capture. The correction 1-zcore reaches 20-35% for alkali metals but falls below 5% for Al and Si, explaining both the failure and success of KS band theory. We derive a closed-form post-SCF formula and validate it for Li, Na, K, Ca, Mg, Al, and Si; the predicted quasiparticle bands resolve the long-standing ARPES bandwidth discrepancy, matching embedded dynamical mean-field theory at negligible cost. This work also exemplifies first-principles agentic science, a direction particularly suited to the AGI-for-Science paradigm: an LLM-co-developed derivation with controlled approximations, verified symbolically and against a few experiments, becomes a deterministic harness for agentic scale-out, resolving simultaneously the LLM audit bottleneck and the non-falsifiability of fit-based AI-for-science.
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