  The exact single-magnon entanglement evolution in Heisenberg chains is
obtained using the Quantum Correlation Transfer Function (QCTF) formulation.
The individual spins' entanglement is given by a hypergeometric function, and
its transient behavior is described via a Bessel function of the first kind.
The presented characterization through the lens of QCTF allowed for calculating
the ballistic single-magnon entanglement edge velocity in Heisenberg chains,
which has not been achieved before. Our results can be extended to the
multi-magnon regime, therefore opening up the means to explain equilibration
dynamics and thermodynamics in Heisenberg chains.
