Photo-induced pattern formations and melting of charge-density-wave order

We investigate the non-equilibrium dynamics of charge-density-wave (CDW) order in the square-lattice Holstein model in response to a pump-probe excitation. At half-filling, the ground state exhibits a checkerboard modulation of particle density. To elucidate the melting of CDW order and the emergence of dynamical inhomogeneities due to pump-probe experiments, we develop an efficient real-space von Neumann equation method for simulating the non-equilibrium dynamics. Our large-scale simulations reveal the melting of CDW order, followed by the formation of complex spatial patterns after the pump-probe experiment. These emergent textures display super density modulations superimposed on the original short-period checkerboard structure. Our findings highlight the role of dynamical inhomogeneity in many-body systems with complex ordered phases induced by photoexcitation, governed by a simple broken $Z_2$ symmetry.