STRONG-COUPLING THEORY FOR THE SPIN-PHONON MODEL

We present a strong-coupling approach to the spin-phonon model with a cubic spectral density, which relies on a matrix representation for th e reduced time evolution operator on the four-dimensional space of pse udospins. The 4 X 4 self-energy matrix Sigma is written as an infinite series in powers of bath fluctuation operators, and the lowest-order approximation is evaluated explicitly. The diagonal element Sigma(zz) corresponds to the result of the noninteracting blip approximation (NI BA); retaining the full matrix is equivalent to taking into account ce rtain blip-blip interactions. Contrary to NIBA, this approach agrees w ith a rigorous result for the quadratic term of the rate. As a main re sult, we find a crossover to incoherent motion at a temperature T, wh ich is compared to previous theoretical work and discussed in view of experimental data for various two-level tunneling systems.