  We consider the Anomalous Hall (AH) state induced by interactions in a
three-orbital per unit-cell model. To be specific we consider a model
appropriate for the Copper-Oxide lattice to highlight the necessary conditions
for time-reversal breaking states which are AH states and which are not. We
compare the singularities of the wave-functions of the three-orbital model,
which are related to the nonzero Berry curvature, and their variation with a
change of gauge to those in the two-orbital model introduced in a seminal paper
by Haldane. Explicit derivation using wave-functions rather than the more
powerful abstract methods may provide additional physical understanding of the
phenomena.
