Unitary transformation with double polaronic generator for spin-boson model: Ground state, thermodynamics and dynamical evolution

Unitary transformation with a double polaronic generator is proposed for the unbiased spin-boson Hamiltonian, which leads to a new ground state with lower ground state energy, as well as an effective Hamiltonian without the counter-rotating coupling. The infrared divergence associated with the nonadiabatic modes in Ohmic bath plays an important role in determining the quantum critical point αc of the ground state, which separates the non-degenerate ground state for α<αc from the degenerate one for α>αc and leads to logarithmic divergence of the bosonic numbers. The thermodynamic properties, the dynamical evolution, and time correlation of the SBM model are studied by the effective Hamiltonian obtained from the unitary transformation, which can be solved easily and transparently by the perturbation theory. As a check of our theoretical treatment and numerical results, we have calculated the Wilson ratio and shown that the spectral sum rule and Shiba's relation are exactly fulfilled.