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

Abstract

Interactions generically have important effects on topological quantum phases. For a quantum anomalous Hall (QAH) insulator, the presence of interactions can qualitatively change a topological phase diagram, which, however, is typically hard to measure in an experiment. Here we propose a scheme based on quench dynamics to detect the mean-field topological phase diagram of an interacting Chern insulator described by the 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 (${t}_{s},{t}_{c}$) capture the emergences of dynamical self-consistent particle density and the dynamical topological phase transition, respectively, while the third one (${t}^{*}$) gives a linear scaling time on the topological phase boundaries. We show generically that the characteristic times obey ${t}_{s}>{t}^{*}>{t}_{c}$ (${t}^{*}<{t}_{s}<{t}_{c}$) in the repulsive (attractive) interacting regime, when the system is quenched from an initial nearly fully polarized state to the topologically nontrivial regimes. Moreover, the Chern number of the equilibrium phase of postquench interacting Hamiltonian can be determined by any two of the three timescales, providing a dynamical way to determine the equilibrium mean-field topological phases. Experimentally, the measurement of ${t}_{s}$ is challenging, while ${t}_{c}$ and ${t}^{*}$ can be directly read out by measuring the spin polarizations of four Dirac points and the time-dependent particle density, respectively, showing the feasibility of the present dynamical scheme. Our work opens a way to detect by quench dynamics the mean-field phase diagram of Chern insulators with interactions.