  Topological quantum phase transition in electron gas systems is an
enthralling phenomena. This phase transition has a unique property in that it
is associated with a quantum phase transition point, which separates different
regions with gapped phases, characterized by an immutable topological quantity
called the Chern number. In this paper, we study a tight binding model for a
three-dimensional topological insulator $(TI)$ thin film that captures
different topological quantum phase transitions in the entire Brillouin zone.
We investigate the effects of a staggered magnetic field, an off-diagonal
coupling term, and a Rashba spin-orbit coupling $(SOC)$ on the topological
insulator thin film model. We give a lucid exposition of the topological phases
by exploring all the topological properties of this system in the entire
Brillouin zone, as a function of the competing interactions. We find that the
system exhibits quantum spin Hall $(QSH)$ phase, quantum anomalous Hall
$(QAH)$, semi-metallic phase, and an ordinary insulator phase. The transition
from one phase to another is invariably associated with a gap closing point. We
further corroborate our results by solving for the edge states modes of the
system.
