  The concurrence between first and the last sites of a fermionic spin chain
containing a single boson is rigorously investigated at finite low temperature
in the vicinity of a weak homogeneous magnetic field. We consider the boson as
a mobile spin-1 particle through the chain and study concurrence without/under
decoherence and express some interesting phase flip and bit flip reactions of
the pairwise entanglement between first and the last half-spins in the chain.
Our investigations show that the concurrence between two considered half-spins
has different behavior for various positions of the single boson along the
chain. Indeed, we realize that the single boson mobility has an essential role
to probe the pairwise entanglement intensity between two spins located at the
opposite ends of a fermionic chain. Interestingly, the entanglement remains
alive for higher temperatures when the boson is the nearest neighbor of the
first fermion. When the boson is at the middle of chain, it is demonstrated
that the threshold temperature (at which the concurrence vanishes) versus
decoherence rate can be considered as a threshold temperature boundary. These
results pave the way to set and interpret the numerical and analytical
expressions for utilizing quantum information in realistic scenarios such as
quantum state transmission, quantum communication science and quantum
information processing, where the both fermion-fermion and fermion-boson
correlations should be taken in to account.
