Vibrational phenomena in glasses at low temperatures captured by field theory of disordered harmonic oscillators

We investigate the vibrational properties of topologically disordered materials by analytically studying particles that harmonically oscillate around random positions. Exploiting field theory in the thermodynamic limit at $T=0$, we build up a self-consistent model by analysing the Hessian utilizing Euclidean Random Matrix theory. In accordance with earlier findings [1], we take non-planar diagrams into account to correctly address multiple local scattering events. By doing so, we end up with a first principles theory that can predict the main anomalies of athermal disordered materials, including the boson peak, sound softening, and Rayleigh damping of sound. In the vibrational density of states, the sound modes lead to Debye's law for small frequencies. Additionally, quasi-localised modes (QLMs), cause an excess in the density of states starting as $\omega^4$ in the low frequency limit.Comment: 6 pages, 5 figures; 7 pages of supplemental informatio