Spatial correlations between atoms can generate a depletion in the energy dispersion of acoustic phonons. Two well-known examples are rotons in superfluid helium and the Kohn anomaly in metals. Here we report on the observation of a large softening of the transverse acoustic mode in quantum paraelectric $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ by means of inelastic neutron scattering. In contrast to other known cases, this softening occurs at a tiny wave vector implying spatial correlation extending over a distance as long as 40 lattice parameters. We attribute this to the formation of mesoscopic fluctuating domains due to the coupling between local strain and ferroelectric fluctuations. Thus, a hallmark of the ground state of insulating $\mathrm{Sr}\mathrm{Ti}{\mathrm{O}}_3$ is the emergence of hybridized optical-acoustic phonons. Mesoscopic fluctuating domains may play a role in quantum tunneling, which impedes the emergence of a finite macroscopic polarization.

• Anharmonic lattice dynamics
• Ferroelasticity
• Ferroelectricity
• Phonons
• Quantum phase transitions
• Insulators
• Paraelectrics
• Relaxor ferroelectrics
• Single crystal materials
• Density functional theory
• First-principles calculations
• Neutron scattering