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(ω) of a 3D model glass former. To magnify the non-Debye sector of the spectrum, we introduce a random pinning field that freezes a finite particle fraction to break the translational invariance and shifts all of the vibrational frequencies of the extended modes toward 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(ω) goes to zero as a power law ωδ(p), with 2 ≤ δ(p) ≤ 4 and δ = 4 above a threshold fraction pth.