Anomalous coarsening and nonlinear diffusion of kinks in an one-dimensional quasi-classical Holstein model

We present a comprehensive study of the phase ordering dynamics in a quasi-classical Holstein model. The ground state of the half-filled system at zero temperature is a commensurate charge density wave (CDW) state with alternating occupied and empty lattice sites. This simplified quasi-classical version of the Holstein model allows us to explicitly investigate the crucial role of electrons in the coarsening dynamics. When the system is subject to a thermal quench, the coarsening of CDW domains is governed by the diffusive motion and annihilation dynamics of kinks, which are topological defects separating the two symmetry-related CDW orders. The size of CDW domains is expected to scale as the square root of time in a standard diffusive dynamics. Yet, our large-scale quench simulations find a slower power-law domain growth with a temperature-dependent exponent. We show that this unusual coarsening dynamics can be attributed to a cooperative hopping phenomenon which results from the conservation of electron number. The correlated-hopping of kinks in turn gives rise to an effective diffusion coefficient that depends on the kink density. We discuss the implications of our results for the phase ordering dynamics of the original Holstein model as well as other functional electron materials.