  In the spin-boson model, the properties of the oscillator bath are fully
characterized by the spectral density of oscillators $J(\omega)$. We study the
case when this function is of Breit-Wigner shape and has a sharp peak at a
frequency $\Omega$ with width $\Gamma\ll\Omega$. We use a number of approaches
such as the weak-coupling Bloch-Redfield equation, the non-interacting blip
approximation (NIBA) and the flow-equation renormalization scheme. We show,
that if $\Omega$ is much larger than the qubit energy scales, the dynamics
corresponds to an Ohmic spin-boson model with a strongly reduced tunnel
splitting. We also show that the direction of the scaling of the tunnel
splitting changes sign when the bare splitting crosses $\Omega$. We find good
agreement between our analytical approximations and numerical results. We
illuminate how and why different approaches to the model account for these
features and discuss the interpretation of this model in the context of an
application to quantum computation and read-out.
