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This paper develops an effective field theory (EFT) of the inhomogeneous electron gas to demonstrate that Kohn-Sham (KS) eigenvalues can be interpreted as quasiparticle bands, renormalized by a frozen-core factor. The EFT reveals that dynamical core excitations, typically frozen out by pseudopotentials, are responsible for the long-standing 20-35% overestimation of ARPES bandwidths by KS band theory in alkali and alkaline-earth metals. A closed-form post-SCF formula is derived and validated on several materials, resolving the ARPES bandwidth discrepancy and matching embedded dynamical mean-field theory results at a significantly reduced computational cost.
Kohn-Sham eigenvalues, often dismissed as unphysical, actually represent quasiparticle bands after accounting for dynamical core excitations, resolving a decades-old discrepancy with ARPES measurements.
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.
