Kohn-Sham Hamiltonian from Effective Field Theory: Quasiparticle Band Narrowing from Frozen Core Dynamics

TL;DR

This paper develops an effective field theory approach to correct Kohn-Sham band energies, explaining discrepancies with experiments and providing a practical formula validated on various materials.

Contribution

It introduces a first-principles derivation linking Kohn-Sham bands to quasiparticle bands via a frozen-core renormalization factor, improving accuracy in band structure predictions.

Findings

KS bands overestimate ARPES bandwidths by 20-35% for alkali metals.

The derived formula accurately predicts quasiparticle bands for multiple elements.

The correction factor explains the success and failure of KS band theory across materials.

Abstract

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.