Dynamical detection of mean-field topological phases in an interacting Chern insulator

Interactions generically have important effects on the topological quantum phases. For a quantum anomalous Hall (QAH) insulator, the presence of interactions can qualitatively change the topological phase diagram which, however, is typically hard to measure in the experiment. Here we propose a novel scheme based on quench dynamics to detect the mean-field topological phase diagram of an interacting Chern insulator described by QAH-Hubbard model, with nontrivial dynamical quantum physics being uncovered. We focus on the dynamical properties of the system at a weak to intermediate Hubbard interaction which mainly induces a ferromagnetic order under the mean-field level. Remarkably, three characteristic times $t_s$, $t_c$, and $t^*$ are found in the quench dynamics. The first two capture the emergence of dynamical self-consistent particle density and dynamical topological phase transition respectively, while the last one gives a linear scaling time on the topological phase boundaries. A more interesting result is that $t_s>t^*>t_c$ ($t^*<t_s<t_c$) occurs in repulsive (attractive) interaction and the Chern number is determined by any two characteristic time scales when the system is quenched from an initial nearly fully polarized state to the topologically nontrivial regimes, showing a dynamical way to determine equilibrium mean-field topological phase diagram via the time scales. Experimentally,the measurement of $t_s$ is challenging while $t_c$ and $t^*$ can be directly readout by measuring the spin polarizations of four Dirac points and the time-dependent particle density, respectively. Our work reveals the novel interacting effects on the topological phases and shall promote the experimental observation.