  In this work, we propose a new and simple model that supports Chern
semimetals. These new gapless topological phases share several properties with
the Chern insulators like a well-defined Chern number associated to each band,
topologically protected edge states and topological phase transitions that
occur when the bands touch each, with linear dispersion around the contact
points. The tight-binding model, defined on the Lieb lattice with
intra-unit-cell and suitable nearest-neighbor hopping terms between three
different species of spinless fermions, supports a single Dirac-like point. The
dispersion relation around this point is fully relativistic and the $3\times3$
matrices in the corresponding effective Hamiltonian satisfy the
Duffin-Kemmer-Petiau algebra. We show the robustness of the topologically
protected edge states by employing the entanglement spectrum. Moreover, we
prove that the Chern number of the lowest band is robust with respect to weak
disorder. For its simplicity, our model can be naturally implemented in real
physical systems like cold atoms in optical lattices.
