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

TL;DR

This paper develops a first-principles field theory model for vibrational properties of disordered glasses at low temperatures, accurately predicting phenomena like the boson peak, sound softening, and Rayleigh damping.

Contribution

It introduces a self-consistent analytical framework using Euclidean Random Matrix theory that accounts for multiple scattering events in disordered harmonic oscillators.

Findings

Predicts the boson peak and sound softening in vibrational density of states.

Shows Debye's law holds for low-frequency sound modes.

Identifies an $ extomega^4$ excess in the density of states due to localized modes.

Abstract

We investigate the vibrational properties of topologically disordered materials by analytically studying particles that harmonically oscillate around random positions. Exploiting classical field theory in the thermodynamic limit at $T=0$, we build up a self-consistent model by analyzing the Hessian utilizing Euclidean Random Matrix theory. In accordance with earlier findings [T. S. Grigera et al.J.~Stat.~Mech.~11 (2011) P02015.], 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, an excess appears in the density of states starting as $\omega^4$ in the low frequency limit, which is attributed to (quasi-) localized modes.