  We construct a model for interacting electrons with strong spin orbit
coupling in the pyrochlore iridates. We establish the importance of the direct
hopping process between the Ir atoms and use the relative strength of the
direct and indirect hopping as a generic tuning parameter to study the
correlation effects across the iridates family. We predict novel quantum phase
transitions between conventional and/or topologically non-trivial phases. At
weak coupling, we find topological insulator and metallic phases. As one
increases the interaction strength, various magnetic orders emerge. The
topological Weyl semi-metal phase is found to be realized in these different
orders, one of them being the all-in/all-out pattern. Our findings establish
the possible magnetic ground states for the iridates and suggest the generic
presence of the Weyl semi-metal phase in correlated magnetic insulators on the
pyrochlore lattice. We discus the implications for existing and future
experiments.
