We discuss the topological phase transition of the spin-$\frac{ 1}{ 2}$ fermionic Haldane model with repulsive on-site interaction. We show that the Berry curvature of the topological Hamiltonian, the first Chern number, and the topological phase transition point can be extracted from the single-particle density matrix for this interacting system. Furthermore, we design a tomography scheme for the single-particle density matrix of interacting fermionic two-band models in experimental realizations with cold atoms in optical lattices.
Categories: cond-mat.quant-gas cond-mat.mes-hall cond-mat.str-el quant-ph