  The low-energy states of quantum many body systems, such as spin chains, are
entangled. Using tensor network computations, we demonstrate a protocol that
distills Bell pairs out of the ground state of the prototypical
transverse-field Ising model. We explore the behavior of rate of entanglement
distillation in various phases, and possible optimizations of the protocol.
Finally, we comment on the protocol as we approach quantum criticality defining
a continuum field theory.
