  We introduce the single-copy entanglement as a quantity to assess quantum
correlations in the ground state in quantum many-body systems. We show for a
large class of models that already on the level of single specimens of spin
chains, criticality is accompanied with the possibility of distilling a
maximally entangled state of arbitrary dimension from a sufficiently large
block deterministically, with local operations and classical communication.
These analytical results -- which refine previous results on the divergence of
block entropy as the rate at which EPR pairs can be distilled from many
identically prepared chains, and which apply to single systems as encountered
in actual experimental situations -- are made quantitative for general
isotropic translationally invariant spin chains that can be mapped onto a
quasi-free fermionic system, and for the anisotropic XY model. For the XX
model, we provide the asymptotic scaling of ~(1/6) log_2(L), and contrast it
with the block entropy. The role of superselection rules on single-copy
entanglement in systems consisting of indistinguishable particles is
emphasized.
