Suppressed coarsening after an interaction quench in the Holstein chain

We investigate the nonequilibrium dynamics induced by an interaction quench in the semiclassical Holstein model within the Ehrenfest nonadiabatic framework, which describes an isolated hybrid quantum-classical system with strictly conserved total energy. Focusing on the half-filled case, where the equilibrium ground state exhibits commensurate charge-density-wave (CDW) order for any nonzero coupling, we identify three distinct post-quench dynamical regimes as a function of the final electron-phonon coupling: a nonequilibrium metallic state without CDW order, an intermediate regime characterized by slow scale-invariant ordering dynamics, and a frozen CDW state with arrested coarsening and immobile kinks. We analyze the intermediate regime in detail and uncover an unconventional algebraic decay of the kink density, $n \sim t^{-1/3}$, distinct from both ballistic annihilation and diffusive coarsening in classical dissipative systems. We show that this anomalous exponent arises from the hybrid nature of the dynamics: while the lattice evolves deterministically, the electronic degrees of freedom act as an effective internal bath that induces diffusive kink motion without energy dissipation. An effective reaction-diffusion description, incorporating both annihilation and elastic scattering of kinks, quantitatively accounts for the observed scaling behavior. Our results reveal a distinct coarsening mechanism in isolated hybrid systems, demonstrating how internal quantum dynamics can qualitatively reshape defect kinetics far from equilibrium.