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

Abstract

Temperature dependence of the effective tunneling frequency of the spin-phonon model for a few particular types of coupling has been studied within the framework of the simple variational method. 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. © 2005 Published by Elsevier B.V.