  Understanding the vibrational and thermal properties of amorphous solids is
one of the most discussed and long-standing issues in condensed matter physics.
Recent works have made significant steps towards understanding harmonic
vibrational states. In particular, it has been established that quasi-localized
vibrational modes emerge in addition to phonon-like vibrational modes. In this
work, we study the anharmonic properties of these vibrational modes. We find
that vibrational modes exhibit anharmonicities that induce particle
rearrangements and cause transitions to different states. These anharmonicities
are distinct from those in crystals, where particle rearrangements never occur.
Remarkably, for both the phonon modes and quasi-localized modes, the
vibrational modes exhibit strong anharmonicities, and the induced particle
rearrangements are always localized in space and are composed of 1 to 1000
particles. Our findings contribute to the understanding of low-temperature
thermal properties, for which anharmonic vibrations are crucial.
