  Na$_2$IrO$_3$ was one of the first materials proposed to feature the
Kane-Mele type topological insulator phase. Contemporaneously it was claimed
that the very same material is in a Mott insulating phase which is described by
the Kitaev-Heisenberg (KH) model. First experiments indeed revealed Mott
insulating behavior in conjunction with antiferromagnetic long-range order.
Further refined experiments established antiferromagnetic order of zigzag type
which is not captured by the KH model. Since then several extensions and
modifications of the KH model were proposed in order to describe the
experimental findings. Here we suggest that adding charge fluctuations to the
KH model represents an alternative explanation of zigzag antiferromagnetism.
Moreover, a phenomenological three-band Hubbard model unifies all the pieces of
the puzzle: topological insulator physics for weak and KH model for strong
electron-electron interactions as well as a zigzag antiferromagnet at
intermediate interaction strength.
