  Solid materials that deviate from the harmonic crystal paradigm exhibit
characteristic anomalies in the specific heat and vibrational density of states
(VDOS) with respect to Debye's theory predictions. The boson peak (BP), a
low-frequency excess in the VDOS over Debye law $g(\omega) \propto \omega^2$,
is certainly the most famous among them; nevertheless, its origin is still
subject of fierce debate. Recent simulation works provided strong evidence that
localized one-dimensional string-like excitations (stringlets) might be the
microscopic origin of the BP. In this work, we study the dynamics of acoustic
phonons interacting with a bath of vibrating 1D stringlets with exponentially
distributed size, as observed in simulations. We show that stringlets strongly
renormalize the phonon propagator and naturally induce a BP anomaly in the
vibrational density of states, corresponding to the emergence of a
dispersionless BP flat mode. Additionally, phonon-stringlet interactions
produce a strong enhancement of sound attenuation and a dip in the speed of
sound near the BP frequency, consistent with experimental and simulation data.
The qualitative trends of the BP frequency and intensity are predicted within
the model and shown to be in good agreement with previous observations. In
summary, our results substantiate with a simple theoretical model the recent
simulation results by Hu and Tanaka claiming the origin of the BP from
stringlet dynamics.
