Anomalous coarsening and nonlinear diffusion of kinks in a one-dimensional quasiclassical Holstein model

We study the phase-ordering dynamics of a quasiclassical Holstein model. At half-filling, the zero-temperature ground state is a commensurate charge-density-wave (CDW) with alternating occupied and empty sites. This quasiclassical formulation enables us to isolate the role of electrons in coarsening dynamics. Following a thermal quench, CDW domains grow through the diffusion and annihilation of kinks-topological defects separating the two symmetry-related CDW orders. While standard diffusive dynamics predicts domain sizes scaling as the square root of time, our large-scale simulations reveal a slower power-law growth with a temperature-dependent exponent. We trace this anomalous behavior to a cooperative kink hopping arising from Fermi-Dirac statistics of electrons and quasiconservation of electron numbers. The correlated-hopping of kinks in turn gives rise to an effective diffusion coefficient that depends on the kink density. These results identify a cooperative kink-hopping mechanism for anomalously slow coarsening in the quasiclassical Holstein model and suggest that similar correlated defect dynamics may also be relevant to phase-ordering processes in related electron-phonon systems.