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Internally-stressed and positionally-disordered minimal complexes yield glasslike nonphononic excitations

Glasses, unlike their crystalline counterparts, exhibit low-frequency nonphononic excitations whose frequencies $ω$ follow a universal $\mathcal{D}\!\left(ω\right)\!\sim\!ω^4$ density of states. The process of glass formation generates positional disorder intertwined with mechanical frustration, posing fundamental challenges in understanding the origins of glassy nonphononic excitations. Here we suggest that \emph{minimal complexes} -- mechanically-frustrated and positionally-disordered local structures -- embody the minimal physical ingredients needed to generate glasslike excitations. We investigate the individual effects of mechanical frustration and positional disorder on the vibrational spectrum of isolated minimal complexes, and demonstrate that ensembles of marginally stable minimal complexes yield $\mathcal{D}\!\left(ω\right)\!\sim\!ω^4$. Furthermore, glasslike excitation emerge by embedding a single minimal complex within a perfect lattice. Consequently, minimal complexes offer a conceptual framework to understand glasslike excitations from first principles, as well as a practical computational method for introducing them into solids.