1307.0868 (A. Churkin et al.)

The strain gap in a system of weak and strong interacting two level
systems    [PDF]

A. Churkin, I. Gabdank, A. Burin, M. Schechter

A system of spatially random, interacting two level systems (TLSs), is considered. The interaction is taken to be random, with spatial dependence of $1/r^3$ at large distances, and a short distance cutoff. The TLSs are divided into two types, differing by the magnitude of their interaction, to model systems such as (i) magnetic insulators, with electronic and nuclear spins interacting via the magnetic dipolar interaction and (ii) glasses and amorphous solids, where inversion symmetric and asymmetric TLSs interact via the dipolar elastic interaction with symmetry dependent interaction strength [M. Schechter and P. C. E. Stamp, arXiv:0910.1283.]. For single species of dipolar interacting TLSs the Efros Shklovskii gap is logarithmic. Here we show that for the Two-TLS model the weakly interacting TLSs are hardly affected by the correlations, and their density of states (DOS) is well approximated by a Gaussian whose width is dictated by their random interaction with the strongly interacting TLSs. In contrast, the strongly interacting TLSs have a power-law reduction in their DOS at low energies. Remarkably, the power-law depends essentially on the short distance cutoff of the interaction. Our results, which are verified using Monte Carlo simulations, suggest that dipolar decoherence in magnetic insulators by electronic spins can be dramatically reduced at temperatures lower than the hyperfine energy. Consequences to the properties of glasses at low temperatures are discussed as well.

View original: http://arxiv.org/abs/1307.0868