  The emergence of the Haldane Chern insulator state due to strong short range
repulsive interactions in the half-filled fermionic spinless honeycomb lattice
model has been proposed and challenged with different methods and yet it still
remains controversial. In this work we revisit the problem using the infinite
density matrix renormalization group method and report numerical evidence
supporting i) the absence of the Chern insulator state, ii) two previously
unnoticed charge ordered phases and iii) the existence and stability of all the
non-topological competing orders that were found previously within mean field.
In addition, we discuss the nature of the corresponding phase transitions based
on our numerical data. Our work establishes the phase diagram of the
half-filled honeycomb lattice model tilting the balance towards the absence of
a Chern insulator phase for this model.
