  We give an analytical description of long distance entanglement (LDE)
mediated by one-dimensional quantum spin chains recently found in numerical
studies. We develop a formalism that allows the computation of LDE for weakly
interacting probes with gapped many-body systems. At zero temperature, a DC
response function determines the ability of the physical system to generate
genuine quantum correlations between the probes. We show that the biquadratic
Heisenberg spin-1 chain is able to produce LDE in the thermodynamical limit and
that the finite antiferromagnetic Heisenberg chain maximally entangles two
spin-1/2 probes very far apart. These results support the current perspective
of using quantum spin chains as entanglers or quantum channels in quantum
information devices.
