A DMRG study of the extended Haldane-Hubbard model

In this work, we study the extended Haldane-Hubbard model at half-filling in a honeycomb lattice. We employ the density matrix renormalization group algorithm in the matrix product state formulation (DMRG-MPS) to obtain the ground state of the system and generate its phase diagram. In agreement with previous results, we find that strong on-site interactions can create a spin density wave phase, whereas strong nearest-neighbor interactions favor a charge density wave phase. A topologically non-trivial phase was also found in the weakly-interacting regime, by measuring the Chern number using a charge-pumping scheme in a finite cylinder geometry. We compare this phase diagram to previous results in the literature obtained via other methods, such as exact diagonalization in small clusters and infinite DMRG, highlighting the similarities and differences in the regions where the phase transitions happen.