Topological bulk and edge correlations of BCS condensate in a two-dimensional singlet-triplet spin pairing model

The condensate of the Bardeen-Cooper-Schrieffer (BCS) pair in the ground state, which may contain information on both topology and spin pairing, promises the superconductivity of the system. In this paper, we study a singlet-triplet spin paring model on a square lattice and investigate the consequences of the competition of on-site and nearest neighbor pairing parameters. We show that the ground state of the system has the form of the condensate of the BCS pair, and the topological transition is associated with the nonanalytic behavior of the pairing order parameters. A real space correlation function on opposite spin direction is introduced to characterizing the topological phase of the many-body ground state. Numerical results demonstrate that this method works well in the presence of disordered perturbation, lattice defects, or irregular boundary conditions. The real space correlation function between two edges of the system is also discussed, which directly reflects the existence of topological edge modes in the many-body ground state.