Universal ratio of TTLS-phonon coupling constants in low-temperature amorphous solids

Tunneling-two-level-system model (TTLS model) has successfully explained several universal properties of amorphous solids at low temperatures. The experimentalists found that the ratios of TTLS-phonon coupling constants γ1/γ1 lie between 1.44 and 1.84 among 16 different amorphous solids, which turns out to be a universal quantity (Berret and Meissner 1988 Z. Phys. B 70 65). However, this universal property remains unexplained. Based on the model introduced by Vural and Leggett (2011 J. Non-Cryst. Solids 357 3528) and real space renormalization, we demonstrate that γ1/γ1 equals to cl/ct, where c _l and c _t are longitudinal and transverse sound velocities, respectively. In this paper, we reveal that this universal quantity γ1/γ1 essentially comes from the mutual interactions between elementary blocks of amorphous solids, and is insensitive to the microscopic material properties. In the appendix, we also make corrections to the many-body interaction of low-temperature amorphous solids derived by Joffrin and Levelut (1975 J. Physique 36 811).