What are the interactions in quantum glasses?

TL;DR

This paper reexamines the low-temperature interactions between defects in quantum glasses, revealing complex couplings including random fields and multiple interaction ranges, which influence defect freezing and dynamics.

Contribution

It provides detailed expressions for defect interactions in quantum glasses, considering second-order couplings and their effects on defect freezing and dynamics.

Findings

Linear coupling causes $1/r^3$ interactions and random fields.

Second-order coupling induces additional random fields and shorter-range interactions.

Active tunneling modes persist at low temperatures, influenced by these interactions.

Abstract

The form of the low-temperature interactions between defects in neutral glasses is reconsidered. We analyse the case where the defects can be modelled either as simple 2-level tunneling systems, or tunneling rotational impurities. The coupling to strain fields is determined up to 2nd order in the displacement field. It is shown that the linear coupling generates not only the usual $1/r^3$ Ising-like interaction between the rotational tunneling defect modes, which cause them to freeze around a temperature $T_G$, but also a random field term. At lower temperatures the inversion symmetric tunneling modes are still active - however the coupling of these to the frozen rotational modes, now via the 2nd-order coupling to phonons, generates another random field term acting on the inversion symmetric modes (as well as shorter-range $1/r^5$ interactions between them). Detailed expressions for all these couplings are given.