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 α, the strength of the ohmic coupling to the environment, and ε, the level asymmetry. This is done by a numerical renormalization group treatment of the related anisotropic Kondo model. For ε=0, the entanglement increases monotonically with α, until it becomes maximal for α→1-. For fixed ε>0, the entanglement is a maximum as a function of α for a value, α=αM<1