Dynamical geometry of the Haldane model under a quantum quench

We explore the time evolution of a topological system when the system undergoes a sudden quantum quench within the same nontrivial phase. Using Haldane's honeycomb model as an example, we show that equilibrium states in a topological phase can be distinguished by geometrical features, such as the characteristic momentum at which the half-occupied edge modes cross, the associated edge-mode velocity, and the winding vector about which the normalized pseudospin magnetic field winds along a great circle on the Bloch sphere. We generalize these geometrical quantities for nonequilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the prequench equilibrium state relaxes to the postquench equilibrium state in an oscillatory fashion, whose amplitude decay as ${t}^{1/2}$. In the process, however, the characteristic winding vector of the nonequilibrium system can evolve to regimes that are not reachable with equilibrium states.