Even-odd parity effects of a spin-1 Heisenberg chain on long-range interaction and entanglement*

A strongly coupled spin chain can be used as a quantum data bus, to mediate long-range interactions and entanglement between remote qubits.By obtaining numerical solutions for finite size systems, we investigate even-odd parity effects in a spin-1 chain and their consequences for long-range interactions and entanglement. We observes some similarities with a spin-1/2 chain~$[1]$. For example, we find that an even-size chain mediates an RKKY (Ruderman-Kittel-Kasuya-Yosida)-like interaction between weakly coupled attached spins, while an odd-size chain acts as a central spin to the attached spins. On the other hand, we find that the RKKY-like interactions have a different character. For a spin-1/2 chain, the interactions decay with qubit separation as they oscillate between ferro and antiferromagnetic couplings. For a spin-1 chain, the interactions also oscillate, but they decay very little as a function of qubit separation. We believe this behavior is a manifestation of the finite Haldane gap of an integer spin chain in the thermodynamic limit.\\[4pt] $[1]$ S. Oh, M. Friesen, X. Hu, Phys. Rev. B {\bf 82}, 140403(R) (2010).