Phase Transition in a Two-State Chain Interacting with a Phonon Bath

The properties of a two-state chain interacting with a phonon bath is studied in this paper. We discuss the renormalization of the single pseudospin tunneling parameter by phonons' interaction, as well as other pseudospins' correlation. We find that for Ohmic dissipation, the correlation between pseudospins vanishes and the phonons' interaction induces the localization–delocalization transition. For our discussed super-Ohmic dissipation, the phonons' interaction only reduces the tunneling parameter and does not induce phase transition. In this case the pseudospins' correlation has its effect and reduces the tunneling parameter at weak coupling. In addition, some application of our results is also discussed.