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The emergence of the Haldane Chern insulator state due to strong short rangerepulsive interactions in the half-filled fermionic spinless honeycomb latticemodel has been proposed and challenged with different methods and yet it stillremains controversial. In this work we revisit the problem using the infinitedensity matrix renormalization group method and report numerical evidencesupporting i) the absence of the Chern insulator state, ii) two previouslyunnoticed charge ordered phases and iii) the existence and stability of all thenon-topological competing orders that were found previously within mean field.In addition, we discuss the nature of the corresponding phase transitions basedon our numerical data. Our work establishes the phase diagram of thehalf-filled honeycomb lattice model tilting the balance towards the absence ofa Chern insulator phase for this model.

Interaction driven phases in the half-filled honeycomb lattice: an infinite density matrix renormalization group study