String-sliding vibrational modes govern the boson peak and phonon anomalies in amorphous materials.

The boson peak is a universal vibrational anomaly of amorphous materials, yet its microscopic origin has remained unclear for decades. Using simulations of ordinary, hyperuniform and unstressed glasses in two and three dimensions, we show that the boson peak originates from the strong resonant coupling-arising from frequency matching-between phonons and intrinsic string-sliding vibrational modes. We identify two classes of excitations with distinct roles: quadrupolar quasi-localized modes (which dominate low-frequency non-affine responses) and string-sliding vibrational modes (which resonate with phonons at terahertz frequencies to generate the boson-peak excess). The boson peak persists even in glasses without quasi-localized modes or associated elastic heterogeneity, whereas phonon anomalies follow directly from this resonance mechanism. Together, these findings establish string-phonon resonance-rather than quasi-localized modes or elastic heterogeneity-as the central microscopic mechanism of the boson peak and provide a unified mode-based framework for understanding and tailoring the vibrational and mechanical properties of amorphous solids.