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 non-equilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the pre-quench equilibrium state relaxes to the post-quench equilibrium state in an oscillatory fashion, whose amplitude decay as $t^{1/2}$. In the process, however, the characteristic winding vector of the non-equilibrium system can evolve to regimes that are not reachable with equilibrium states.