Dynamic and thermodynamic properties of a spin-boson system

A two-level system with a transverse linear infrared singular coupling to a boson gas is treated within a mode-coupling approximation for the dynamics. Static spin susceptibilities and spin polarizations are evaluated consistently with the dynamics by exploiting sum rules. The spin energy is obtained by integration over the excitation spectrum of the boson scattering matrix. In case of a high-frequency boson cutoff large compared to the level splitting, the results demonstrate pronounced precursor phenomena for the known zero-temperature phase transition of the model. In the opposite case the results are in semiquantitative agreement with previous numerical findings for the transition to self-trapping obtained by DeRaedt and DeRaedt.