  The Haldane model of the Chern insulator is considered on the Lieb and
honeycomb lattices. We provide a detailed analysis of the model's ground-state
phase diagram and demonstrate a scenario of the topological phase transitions
in the system with a single-particle spectrum that includes flat and dispersion
bands, that is realized on the Lieb lattice. We find that the Chern number of
the flat band is non-zero, depending on the parameters of the model. We define
the topological metal state as an intermediate state between topological
insulator and trivial metal. The phase transition between topological insulator
and topological metal states is accompanied by continuous changing of the Chern
number, a jump of the surface charge or spin current defines the point of the
topological metal-trivial metal phase transition. The results have been
illustrated with numerical calculations of the model.
