Analytic results on long distance entanglement mediated by gapped spin chains

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.