The effect of interactions and disorder on the relaxation of two-level systems in amorphous solids

TL;DR

This paper models the low-temperature relaxation dynamics of amorphous solids' two-level systems considering disorder and interactions, revealing how these factors influence the speed of relaxation processes.

Contribution

It introduces a TLS-glass model based on the random field Ising model with long-range interactions, extending previous electron-glass studies to amorphous solids.

Findings

Relaxation rates follow a 1/λ distribution, causing logarithmic slow relaxation.

Increased interactions slow down electron-glass dynamics but speed up TLS-glass relaxation.

System-specific properties determine whether interactions slow down or accelerate glass dynamics.

Abstract

At low temperatures the dynamical degrees of freedom in amorphous solids are tunnelling two-level systems (TLSs). Concentrating on these degrees of freedom, and taking into account disorder and TLS-TLS interactions, we obtain a "TLS-glass", described by the random field Ising model with random $1/r^3$ interactions. In this paper we perform a self consistent mean field calculation, previously used to study the electron-glass (EG) model [A.~Amir {\it et al.}, Phys. Rev. B {\bf 77}, 165207, (2008)]. Similar to the electron-glass, we find $\frac{1}{\lambda}$ distribution of relaxation rates $\lambda$, leading to logarithmic slow relaxation. However, with increased interactions the EG model shows slower dynamics whereas the TLS glass model shows faster dynamics. This suggests that given system specific properties, glass dynamics can be slowed down or sped up by the interactions.