Calculation of crystal defects induced in CaWO$_{4}$ by 100 eV displacement cascades using a linear Machine Learning interatomic potential

We determine the energy stored in the crystal defects induced by $\mathcal{O}(10-100)$\,eV nuclear recoils in low-threshold CaWO$_{4}$ cryogenic detectors. A Machine Learning interatomic potential is developed to perform molecular dynamics simulations. We show that the energy spectra expected from Dark Matter and neutrino coherent scattering are affected by the crystal defects and we provide reference predictions. We discuss the special case of the spectrum of nuclear recoils induced by neutron capture, which could offer a unique sensitivity to the calculated stored energies.