  The entanglement and quantum correlation measures have been investigated for
the ground state of a spin chain with a Kitaev-type exchange interactions on
alternating bonds, along with a transverse magnetic field. There is a
macroscopic degeneracy in the ground state for zero magnetic field, implying a
quantum critical point. But peculiarly in this model, the entanglement measures
do not show any singular behavior in the vicinity of the critical point, as
seen in the transverse Ising model ground state and related models. We have
investigated different correlation measures analytically, that have been used
for many solvable spin systems to track a quantum critical point. We compute
the pair concurrence measure of entanglement, the pair quantum discord to track
the quantum correlations, and a global entanglement measure and a multi-species
entanglement measure to investigate multi-party entanglement, both analytically
and numerically. The nearest-neighbor concurrence shows a peak structure as a
function of magnetic field, near the critical point, for various values of the
ratio of interaction strengths, but its derivative does not show a singular
behavior close to the critical point. A similar behavior is shown by the
quantum discord and the global entanglement. The multi-species entanglement
shows the most-pronounced signature of the critical point, in its first-order
derivative, though the entanglement and its derivatives have a smooth behavior
in the critical region.
