  We study the lattice dynamics of iron superconductor FeSe, and address the
fundamental question of how important is proper description of fluctuating
magnetic moments in metallic systems for phonon dispersion and phonon density
of states. We show that Density Functional Theory (DFT)+ embedded Dynamical
Mean-Field Theory (eDMFT) functional approach, which truly captures the
fluctuating local moments, largely eliminates the deficiency of DFT for
description of lattice dynamics in correlated metallic systems, and predicts
phonon dispersion and phonon density of states in very good agreement with
available X-ray data and nuclear inelastic scattering. This benchmark between
eDMFT and experiment will be important for data science-driven material design,
in which DFT is being replaced by beyond DFT methods.
