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 neighbour interactions. We find evidence for a charge density wave phase, a Kekul\'e 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.
@article{arxiv.1308.6094,
title = {Interaction driven phases in the honeycomb lattice from exact diagonalization},
author = {Noel A. García-Martínez and Adolfo G. Grushin and Titus Neupert and Belén Valenzuela and Eduardo V. Castro},
journal= {arXiv preprint arXiv:1308.6094},
year = {2013}
}