  We present a model for a Chern insulator on the square lattice with complex
first and second neighbor hoppings and a sublattice potential which displays an
unexpectedly rich physics. Similarly to the celebrated Haldane model, the
proposed Chern insulator has two topologically non-trivial phases with Chern
numbers $\pm1$. As a distinctive feature of the present model, phase
transitions are associated to Dirac points that can move, merge and split in
momentum space, at odds with Haldane's Chern insulator where Dirac points are
bound to the corners of the hexagonal Brillouin zone. Additionally, the
obtained phase diagram reveals a peculiar phase transition line between two
distinct topological phases, in contrast to the Haldane model where such
transition is reduced to a point with zero sublattice potential. The model is
amenable to be simulated in optical lattices, facilitating the study of phase
transitions between two distinct topological phases and the experimental
analysis of Dirac points merging and wandering.
