Characterization of Quantum and Classical Critical Points for an Integrable Two-Qubit Spin-Boson Model

The class of two-interacting-qubit spin-boson models with vanishing transverse fields on the spin-pair is studied. The model can be mapped exactly into two independent standard single-impurity spin-boson models where the role of the tunneling parameter is played by the spin-spin coupling. The dynamics of the magnetization are analyzed for different levels of (an)isotropy. The existence of a decoherence-free subspace, as well as of different classical regimes separated by a critical temperature, and symptoms of quantum (first-order and Kosterlitz-Thouless type) phase transitions in the Ohmic regime are brought to light.