Phase diagram and quench dynamics of a periodically driven Haldane model

We investigate a periodically driven Haldane model subjected to a two-stage driving scheme in the form of a step function. By using the Floquet theory, we obtain the topological phase diagram of the system. We also find that anomalous Floquet topological phases exist in the system. Focusing on examining the quench dynamics among topological phases, we analyze the site distribution of the 0-mode and π-mode edge states in long-period evolution after a quench. The results demonstrate that, under certain conditions, the site distribution of the 0-mode can be confined at the edge even in long-period evolution. Additionally, both the 0-mode and π-mode can recover and become confined at the edge in long-period evolution when the post-quench parameters $\left(T,{\displaystyle \frac{M_2}{M_1}}\right)$ in the phase diagram cross away from the phase boundary ${\displaystyle \frac{M_2}{M_1}}={\displaystyle \frac{6\sqrt{3}{t}_2}{M_1}}-1$. Furthermore, we conclude that whether the edge state is confined at the edge in the long-period evolution after a quench depends on the similarity of the edge states before and after the quench. Our findings reveal some new characteristics of quench dynamics in a periodically driven system.