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

TL;DR

This paper investigates the slow coarsening dynamics of charge-density-wave domains in a quasi-classical Holstein model, revealing anomalous diffusion caused by electron statistics and kink interactions, with implications for electron-phonon systems.

Contribution

It introduces a novel mechanism for slow domain growth driven by cooperative kink hopping influenced by electron statistics in a quasi-classical Holstein model.

Findings

Domain growth follows a temperature-dependent power law slower than standard diffusion.

Kink hopping is cooperative and affected by Fermi-Dirac statistics.

Effective diffusion coefficient depends on kink density, leading to anomalous coarsening.

Abstract

We study the phase-ordering dynamics of a quasi-classical Holstein model. At half-filling, the zero-temperature ground state is a commensurate charge-density-wave (CDW) with alternating occupied and empty sites. This quasi-classical 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 quasi-conservation 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 uncover a new mechanism for slow coarsening and carry implications for phase-ordering in the full Holstein model and related electron-phonon systems.