Measuring an interaction-induced topological phase transition via the single-particle density matrix

Interaction-induced topologically nontrivial phases have been theoretically predicted and need more experimental verification. Cold atom systems with tunable interaction strength provide a flexible platform for studying these effects. Here, we focus on the experimental signature of topological phase and topological phase transition (TPT). Since the topological Hamiltonian carries the information of the topology of the system, we first establish its relation to the single-particle density matrix (SPDM) for interacting two-band systems, and then design a tomography scheme for the SPDM in cold atom experiments. Thus the Berry curvature of the topological Hamiltonian, the Chern number, and the TPT point can be reconstructed from experimental data.