Quantum Phases in a Two-Dimensional Generalized interacting SSH Model

We study interaction-driven quantum phases in a two-dimensional generalized Su-Schrieffer-Heeger (SSH) defined on a square lattice with inequivalent nearest-neighbor hopping, next-nearest-neighbor hopping and a staggered on-site potential. In the non-interacting limit, the model hosts either a quadratic band touching (QBT) at the Brillouin-zone center or symmetry-protected Dirac nodes, depending on microscopic parameters. In the parameter regime with a QBT, our self-consistent Hartree-Fock analysis shows that weak to intermediate interactions can spontaneously break time-reversal symmetry and stabilize a quantum anomalous Hall (QAH) insulating phase with a finite Chern number. Interestingly, this QAH phase is found to weakly break lattice-symmetries, leading to a small but finite nematic bond order. This is in contrast to the standard QAH phase in checkerboard lattice, which preserves all lattice symmetries. Additionally, we find an enhanced bond-nematic Dirac semimetallic (BNDS) phase due to asymmetric hopping, which is thought to be absent in the Hartree-Fock approach. In the parameter regimes where QBT splits into two Dirac nodes, the QAH phase survives up to a finite staggered on-site potential. However, as the staggered potential increases, the QAH phase is suppressed while the BNDS phase grows stronger.