Acoustic interactions between inversion symmetric and asymmetric two-level systems

TL;DR

This paper investigates how inversion symmetric and asymmetric two-level systems in disordered lattices interact via phonons, revealing how their interactions depend on symmetry and disorder, and supporting the two-TLS model for universality in amorphous solids.

Contribution

It provides numerical calculations of TLS-TLS interactions in disordered lattices, highlighting the role of symmetry and disorder, and supports the two-TLS model explaining universality in phonon attenuation.

Findings

Interaction magnitude depends on TLS symmetry.

Disorder alters the spatial power law of interactions.

Results align with the two-TLS model for universality.

Abstract

Amorphous solids, as well as many disordered lattices, display remarkable universality in their low temperature acoustic properties. This universality is attributed to the attenuation of phonons by tunneling two-level systems (TLSs), facilitated by the interaction of the TLSs with the phonon field. TLS-phonon interaction also mediates effective TLS-TLS interactions, which dictates the existence of a glassy phase and its low energy properties. Here we consider KBr:CN, the archetypal disordered lattice showing universality. We calculate numerically, using conjugate gradients method, the effective TLS-TLS interactions for inversion symmetric (CN flips) and asymmetric (CN rotations) TLSs, in the absence and presence of disorder, in two and three dimensions. The observed dependence of the magnitude and spatial power law of the interaction on TLS symmetry, and its change with disorder, characterizes TLS-TLS interactions in disordered lattices in both extreme and moderate dilutions. Our results are in good agreement with the two-TLS model, recently introduced to explain long-standing questions regarding the quantitative universality of phonon attenuation and the energy scale of $\approx 1-3$ K below which universality is observed.