We develop a self-consistent first-principles framework for determining the screened Coulomb interaction strength (U) based on constrained dynamical mean-field theory (cDMFT). Unlike conventional approaches, this method incorporates essential vertex corrections within the same embedded-DMFT formalism used for the electronic structure calculation. Using the cDMFT-derived interaction strengths as input to embedded DMFT yields spectral functions in excellent agreement with photoemission experiments across a wide range of materials, spanning 3d to 5d transition-metal compounds, including correlated metals, Mott insulators, altermagnets, and unconventional superconductors. This unified many-body framework establishes a systematic first-principles route for determining interaction strengths in correlated materials and substantially enhances the predictive power of DFT+DMFT and its extensions.
@article{arxiv.2601.12678,
title = {Self-Consistent Coulomb Interactions from Embedded Dynamical Mean-Field Theory},
author = {Antik Sihi and Subhasish Mandal and Kristjan Haule},
journal= {arXiv preprint arXiv:2601.12678},
year = {2026}
}