Topological phases of spinless p-orbital fermions in zigzag optical lattices

Motivated by the experiment [St-Jean et al., Nat. Photonics 11, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless p-orbital fermions with local interorbital hoppings and repulsive interactions between p(x) and p(y) bands in zigzag optical lattices. We show that spinless p-band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state phases and quantum phase transitions of the model. This work provides a simple scheme to simulate topological phases and the quench dynamics of many-body systems in optical lattices.