Here we introduce a new approach to compute the finite temperature lattice dynamics from first-principles via the newly developed slave mode expansion. We study PbTe where inelastic neutron scattering (INS) reveals strong signatures of nonlinearity a
s evidenced by anomalous features which emerge in the phonon spectra at finite temperature. Using our slave mode expansion in the classical limit, we compute the vibrational spectra and show remarkable agreement with temperature dependent INS measurements. Furthermore, we resolve experimental controversy by showing that there are no appreciable local nor global spontaneously broken symmetries at finite temperature and that the anomalous spectral features simply arise from two anharmonic interactions. Our approach should be broadly applicable across the periodic table.
