  We investigate the entanglement between a spin and its environment in
impurity systems which exhibit a second-order quantum phase transition. As an
application, we employ the spin-boson model, describing a two-level system
(spin) coupled to a subohmic bosonic bath with power-law spectral density,
${\cal J}(\omega)\propto \omega^s$ and $0<s<1$. Combining Wilson's Numerical
Renormalization Group method and hyperscaling relations, we demonstrate that
the entanglement between the spin and its environment is always enhanced at the
quantum phase transition resulting in a visible cusp (maximum) in the entropy
of entanglement. We formulate a correspondence between criticality and impurity
entanglement entropy, and the relevance of these ideas to Nano-systems is
outlined.
