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Charge-density wave phases in quantum materials stem from the complexinterplay of electronic and lattice degrees of freedom. Nowadays, varioustime-resolved spectroscopy techniques allow to actively manipulate such phasesand monitor their dynamics in real time. Modeling such nonequilibrium dynamicstheoretically is a great challenge and exact methods can usually only treat asmall number of atoms and finitely many phonons. We approach the melting ofcharge-density waves in a Holstein model after a sudden switch-on of theelectronic hopping from two perspectives: We prove that in the non-interactingand in the strong-coupling limit, the CDW order parameter on high-dimensionalhypercubic lattices obeys a factorization relation for long times, such thatits dynamics can be reduced to the one-dimensional case. Secondly, we presentnumerical results from semiclassical techniques based on the Truncated WignerApproximation for two spatial dimensions. A comparison with exact data obtainedfor a Holstein chain shows that a semiclassical treatment of both the electronsand phonons is required in order to correctly describe the phononic dynamics.This is confirmed, in addition, for a quench in the electron-phonon couplingstrength.

Quench dynamics in higher-dimensional Holstein models: Insights from Truncated Wigner Approaches