Probing the non-Debye low frequency excitations in glasses through random pinning

We investigate the properties of the low-frequency spectrum in the density of states $D(\omega)$ of a three-dimensional model glass former. To magnify the Non-Debye sector of the spectrum, we introduce a random pinning field that freezes a finite particle fraction in order to break the translational invariance and shifts all the vibrational frequencies of the extended modes towards higher frequencies. We show that Non-Debye soft localized modes progressively emerge as the fraction $p$ of pinned particles increases. Moreover, the low-frequency tail of $D(\omega)$ goes to zero as a power law $\omega^{\delta(p)}$, with $2 \!\leq \! \delta(p) \!\leq\!4$ and $\delta\!=\!4$ above a threshold fraction $p_{th}$.