Interaction-driven phases in the half-filled spinless honeycomb lattice from exact diagonalization

We investigate the fate of interaction-driven phases in the half-filled honeycomb lattice for finite systems via exact diagonalization with nearest- and next-nearest-neighbor interactions. We find evidence for a charge density wave phase, a Kekule bond order, and a sublattice charge-modulated phase in agreement with previously reported mean-field phase diagrams. No clear sign of an interaction-driven Chern insulator phase (Haldane phase) is found despite being predicted by the same mean-field analysis. We characterize these phases by their ground-state degeneracy and by calculating charge-order and bond-order correlation functions.