Extended Data Figure 1: Nonlinear lattice dynamics in the limit of cubic and quartic coupling.

Dashed lines: potential energy of a mode Q_R as a function of mode amplitude. a, A static distortion shifts the potential of all modes Q_R that are coupled through a coupling (solid line), displacing the equilibrium position towards a new minimum. b, Owing to quartic coupling, the energy potential of a coupled mode Q_j is deformed symmetrically on static distortion . The frequency of the mode first softens until it is destabilized, which manifests in a double well potential (solid line).