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.

6 pages, 3 figures