  We have investigated the zero and finite temperature behaviors of the
anisotropic antiferromagnetic Heisenberg XXZ spin-1/2 chain in the presence of
a transverse magnetic field (h). The attention is concentrated on an interval
of magnetic field between the factorizing field (h_f) and the critical one
(h_c). The model presents a spin-flop phase for 0<h<h_f with an energy scale
which is defined by the long range antiferromagnetic order while it undergoes
an entanglement phase transition at h=h_f. The entanglement estimators clearly
show that the entanglement is lost exactly at h=h_f which justifies different
quantum correlations on both sides of the factorizing field. As a consequence
of zero entanglement (at h=h_f) the ground state is known exactly as a product
of single particle states which is the starting point for initiating a spin
wave theory. The linear spin wave theory is implemented to obtain the specific
heat and thermal entanglement of the model in the interested region. A double
peak structure is found in the specific heat around h=h_f which manifests the
existence of two energy scales in the system as a result of two competing
orders before the critical point. These results are confirmed by the low
temperature Lanczos data which we have computed.
