  We study the field dependence of the entanglement of formation in anisotropic
S=1/2 antiferromagnetic chains displaying a T=0 field-driven quantum phase
transition. The analysis is carried out via Quantum Monte Carlo simulations. At
zero temperature the entanglement estimators show abrupt changes at and around
criticality, vanishing below the critical field, in correspondence with an
exactly factorized state, and then immediately recovering a finite value upon
passing through the quantum phase transition. At the quantum critical point, a
deep minimum in the pairwise-to-global entanglement ratio shows that multi-spin
entanglement is strongly enhanced; moreover this signature represents a novel
way of detecting the quantum phase transition of the system, relying entirely
on entanglement estimators.
