Single-copy entanglement in critical quantum spin chains

We consider 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 maximally entangled pairs can be distilled from many identically prepared chains---are made quantitative for general isotropic translationally invariant spin chains that can be mapped onto a quasifree fermionic system, and for the anisotropic $XY$ model. For the $XX$ model, we provide the asymptotic scaling of $\ensuremath{\sim}(1∕6){\mathrm{log}}_{2}(L)$, and contrast it with the block entropy.