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Perturbation Approach for the Localization Transition in the Dissipative Two-State System

Analysis of a dissipative two-state system at zero temperature shows that the model Hamiltonian may be exactly reduced to a modified quantum sine-Gordon model, which describes the effective interactions between the low-frequency phonons under coupling with a tunneling system. Directly considering the infrared divergence encountered in the conventional perturbation treatment, we have developed a new perturbation approach for the effective Hamiltonian, and derived the exact critical conditions for the localization transition. In the critical regime, a gap will be opened near zero momentum in the elementary excitation spectrum of the low-frequency phonons, and the corresponding ground state wave function is found to be a pairing quasi-particle state, analogous to the BCS superconducting state.