  One-dimensional spin-1/2 systems are well-known candidates to study the
quantum correlations between particles. In the condensed matter physics,
studies often are restricted to the 1st neighbor particles. In this work, we
consider the 1D XXZ model in a transverse magnetic field (TF) which is not
integrable except at specific points. Analytical expressions for quantum
correlations (entanglement and quantum discord) between spin pairs at any
distance are obtained for both zero and finite temperature, using an analytical
approach proposed by Caux et al. [PRB 68, 134431 (2003)]. We compare the
efficiency of the QD with respect to the entanglement in the detection of
critical points (CPs) as the neighboring spin pairs go farther than the next
nearest neighbors. In the absence of the TF and at zero temperature, we show
that the QD for spin pairs farther than the 2nd neighbors is able to capture
the critical points while the pairwise entanglement is absent. In contrast to
the pairwise entanglement, two-site quantum discord is effectively long-range
in the critical regimes where it decays algebraically with the distance between
pairs. We also show that the thermal quantum discord between neighbor spins
possesses strong distinctive behavior at the critical point that can be seen at
finite temperature and, therefore, spotlights the critical point while the
entanglement fails in this task.
