# Transverse optical phonon branch curvature

Cubic PbTe keeps a centrosymmetric average structure yet hosts finite-range local polar correlations, which were often attributed to lattice anharmonicity. Machine-learned interatomic potentials trained on density functional theory data drive 100,000-atom-scale molecular dynamics, and mapping them onto an interpretable force-constant model lets third- and fourth-order terms be switched off. The nanoscale correlations persist without those anharmonic terms, but vanish when harmonic interactions are cut to the third nearest neighbor; at low temperature the correlation range exceeds 50 Å.

Cubic PbTe keeps a centrosymmetric average structure yet hosts finite-range local polar correlations, which were often attributed to lattice anharmonicity. Machine-learned interatomic potentials trained on density functional theory data drive 100,000-atom-scale molecular dynamics, and mapping them onto an interpretable force-constant model lets third- and fourth-order terms be switched off. The nanoscale correlations persist without those anharmonic terms, but vanish when harmonic interactions are cut to the third nearest neighbor; at low temperature the correlation range exceeds 50 Å.