Thermodynamics of the dissipative two-state system: A Bethe-ansatz study

The thermodynamics of the dissipative two-state system is calculated exactly for all temperatures and level asymmetries for the case of Ohmic dissipation. We exploit the equivalence of the two-state system to the anisotropic Kondo model and extract the thermodynamics of the former by solving the thermodynamic Bethe-ansatz equations of the latter. The universal scaling functions for the specific heat $C_{\alpha }\mathrm{}\left(T\right)\mathrm{}$ and static dielectric susceptibility ${\chi }_{\alpha }\mathrm{}\left(T\right)\mathrm{}$ are extracted for all dissipation strengths $0<\mathrm{}\alpha <1.\mathrm{}$ The logarithmic corrections to these quantities at high temperatures are found in the Kondo limit $\overrightarrow{\alpha }{1}^{-},$ whereas for $\alpha <1\mathrm{}$ we find the expected power law temperature dependences with the powers being functions of the dissipative coupling α. The low-temperature behavior is always that of a Fermi liquid.