  Low-temperature properties of crystalline solids can be understood using
harmonic perturbations around a perfect lattice, as in Debye's theory.
Low-temperature properties of amorphous solids, however, strongly depart from
such descriptions, displaying enhanced transport, activated slow dynamics
across energy barriers, excess vibrational modes with respect to Debye's theory
(i.e., a Boson Peak), and complex irreversible responses to small mechanical
deformations. These experimental observations indirectly suggest that the
dynamics of amorphous solids becomes anomalous at low temperatures. Here, we
present direct numerical evidence that vibrations change nature at a
well-defined location deep inside the glass phase of a simple glass former. We
provide a real-space description of this transition and of the rapidly growing
time and length scales that accompany it. Our results provide the seed for a
universal understanding of low-temperature glass anomalies within the
theoretical framework of the recently discovered Gardner phase transition.
