  We investigate the nonequilibrium dynamics of the spinless Haldane model with
nearest-neighbor interactions on the honeycomb lattice by employing an unbiased
numerical method. In this system, a first-order transition from the Chern
insulator (CI) at weak coupling to the charge-density-wave (CDW) phase at
strong coupling can be characterized by a level crossing of the lowest energy
levels. Here we show that adiabatically following the eigenstates across this
level crossing, their Chern numbers are preserved, leading to the
identification of a topologically-nontrivial low-energy excited state in the
CDW regime. By promoting a resonant energy excitation via an ultrafast
circularly polarized pump pulse, we find that the system acquires a
non-vanishing Hall response as a result of the large overlap enhancement
between the time-dependent wave-function and the topologically non-trivial
excited state. This is suggestive of a photoinduced topological phase
transition via unitary dynamics, despite a proper definition of the Chern
number remaining elusive for an out-of-equilibrium interacting system. We
contrast these results with more common quench protocols, where such features
are largely absent in the dynamics even if the post-quench Hamiltonian displays
a topologically nontrivial ground state.
