Nature of Localization-Delocalization Transition in a Two-Level System Interacting with a Phonon Bath: a Variational Treatment with an Improved Wave Function

A two-level system interacting with a phonon bath is studied using a variational method with an improved trial wave function. It is shown that our results for the ground state energy are in general lower than those obtained by other similar variational methods. It is also demonstrated that there are two possible ground states for the system, one for smaller values of the tunneling matrix element and the other for larger values of it and the system undergoes a localization-delocalization transition as the tunneling matrix element is increased beyond a critical value. Though, in general, there is no dispute about the existence of this transition, the nature of the transition is still not very clear. In the present work, we show, in contrast to the other variational results, that localization-delocalization transition is always smooth in conformity the exact numerical results.