Thermodynamics of dissipative two-level system: A perturbation approach based on unitary transformation

The thermodynamics of a dissipative two-level system is studied by means of the perturbation approach based on a unitary transformation. Both the Ohmic and non-Ohmic dissipative heat-bath are treated. Analytical results for entropy, specific heat, and static susceptibility are obtained for the scaling limit Δ/ωc≪1Δ/ωc≪1 as well as the general 0<Δ/ωc<10<Δ/ωc<1 case. For the sub-Ohmic bath the transition between the delocalized and localized phase is discussed. Our approach is quite simple and yet it gives correct thermodynamics for the lower-temperature region and weak coupling case.