Kohn-Sham Bandwidth Correction via Effective Field Theory

A new effective field theory (EFT) for the inhomogeneous electron gas explains why Kohn-Sham (KS) bandwidths overestimate angle-resolved photoemission (ARPES) measurements by 20-35% in alkali and alkaline-earth metals. The discrepancy, persistent across all exchange-correlation functionals, is attributed to a frozen-core renormalization factor zcore that captures dynamical core excitations conventional pseudopotentials miss. The correction 1-zcore reaches 20-35% for alkali metals, matching experimental data. The EFT requires two conditions: scale separation between core excitation energies and valence Fermi energy, and approximate Galilean invariance of the uniform electron gas, confirmed by diagrammatic Monte Carlo. This work provides a rigorous physical interpretation for KS eigenvalues, which density functional theory (DFT) assigns no meaning, and offers a systematic correction for many-body methods and ARPES comparisons.