  We investigate the static and dynamical patterns of entanglement in an
anisotropic XY model with an alternating transverse magnetic field, which is
equivalent to a two-component one-dimensional Fermi gas on a lattice, a system
realizable with current technology. Apart from the antiferromagnetic and
paramagnetic phases, the model possesses a dimer phase which is not present in
the transverse XY model. At zero temperature, we find that the first derivative
of bipartite entanglement can detect all the three phases. We analytically show
that the model has a "factorization line" on the plane of system parameters, in
which the zero temperature state is separable. Along with investigating the
effect of temperature on entanglement in a phase plane, we also report a
non-monotonic behavior of entanglement with respect to temperature in the
anti-ferromagnetic and paramagnetic phases, which is surprisingly absent in the
dimer phase. Since the time dynamics of entanglement in a realizable physical
system plays an important role in quantum information processing tasks, the
evolutions of entanglement at small as well as large time are examined.
Consideration of large time behavior of entanglement helps us to prove that in
this model, entanglement is always ergodic. We observe that other quantum
correlation measures can qualitatively show similar features in zero and finite
temperatures. However, unlike nearest-neighbor entanglement, the
nearest-neighbor information theoretic measures can be both ergodic as well as
non-ergodic, depending on the system parameters.
