Entanglement between a qubit and the environment in the spin-boson model

The quantitative description of the quantum entanglement between a qubit and its environment is considered. Specifically, for the ground state of the spin-boson model, the entropy of entanglement of the spin is calculated as a function of alpha, the strength of the ohmic coupling to the environment, and epsilon, the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For epsilon=0, the entanglement increases monotonically with alpha, until it becomes maximal for alpha-->1(-). For fixed epsilon>0, the entanglement is a maximum as a function of alpha for a value, alpha=alpha(M)<1.