Finite temperature variational analysis of the tunneling and localization in spin-phonon model

Our analysis shows that for the Ohmic type of coupling, temperature drives the system towards delocalization. The same type of behavior has been noticed for super-Ohmic case, but in the so-called “adiabatic regime”, while in the nonadiabatic case we predict localization transition, analogous to that observed for Ohmic coupling, when temperature dependent coupling constant S(T) approaches critical value S(T)∼1/2. In contrast to these results, for super-Ohmic (r=3) case, there was no substantial difference with respect to zero-temperature case. Brief discussion of the validity of the method has been given.