Effects of correlations on phase diagrams of the two-dimensional Su–Schrieffer–Heeger model with the larger topological invariant

For the Su–Schrieffer–Heeger (SSH) model on the two-dimensional square lattice, two third nearest neighbor hoppings which preserve chiral symmetry are introduced. Like the case of one dimension, the longer-range hopping can drive topological transitions and leads to the larger topological invariant (vectored Berry phase for the two dimensional SSH model). We obtain the phase boundaries and topological phase diagrams from the winding pattern of $\rho \left(k_l\right)$ of the Bloch Hamiltonian. The energy spectra and edge modes of the finite-sized model are also obtained. Effects of correlations on the extended two dimensional SSH model are investigated. The correlation shifts the phase boundaries and leads to topological transitions. Several special points in non-interacting phase diagrams are chosen to illustrate the different phase transitions and a correlations-driven topologically non-trivial phase from the trivial one is found. In this work, the slave-rotor mean field method is applied to the interacting model and we focus on the case of physical electrons, i.e. the Mott transition of charge degree of freedom is avoided in our investigations.