Entanglement distillation from the vacuum of quantum spin chains

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.