  A hallmark of structural glasses and other disordered solids is the emergence
of excess low-frequency vibrations, on top of the Debye spectrum $D_{\rm
Debye}(\omega)$ of phonons ($\omega$ denotes the vibrational frequency), which
exist in any solid whose Hamiltonian is translationally invariant. These excess
vibrations -- a signature of which is a THz peak in the reduced density of
states $D(\omega)/D_{\rm Debye}(\omega)$, known as the boson peak -- have
resisted a complete theoretical understanding for decades. Here, we provide
direct numerical evidence that vibrations near the boson peak consist of
hybridizations of phonons with many quasilocalized excitations, the latter were
recently shown to generically populate the low-frequency tail of the
vibrational spectra of structural glasses quenched from a melt and of
disordered crystals. Our results suggest that quasilocalized excitations exist
up to and in the vicinity of the boson-peak frequency, and hence constitute
fundamental building blocks of the excess vibrational modes in glasses.
