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.

💡 Research Summary

In this work the authors study the nonequilibrium dynamics of the one‑dimensional semiclassical Holstein model after a sudden interaction quench, using an energy‑conserving Ehrenfest non‑adiabatic framework. The lattice degrees of freedom are treated as classical harmonic oscillators obeying Hamilton’s equations, while the spinless electrons evolve under the von Neumann equation for the single‑particle density matrix. Because the electronic Hamiltonian remains quadratic, the electronic state stays a Slater determinant, allowing large‑scale simulations (thousands of sites, long times) while preserving strict total‑energy conservation.

The system is prepared at half‑filling in a uniform metallic state (zero lattice distortion, average density ½). At time t = 0 the electron‑phonon coupling g is abruptly changed to a final value g_f. Depending on g_f three distinct dynamical regimes emerge:

1. Metallic regime (weak g_f). The final coupling is below the CDW instability threshold; the lattice remains essentially undistorted, the electronic spectrum stays metallic, and no domain walls (kinks) form. The system quickly settles into a stationary nonequilibrium metallic state with no long‑range order.

2. Quasi‑coarsening regime (intermediate g_f). Here g_f exceeds the CDW threshold but is not so large that the lattice instantly locks into a perfect charge‑density‑wave pattern. The lattice distortion grows, forming alternating domains of opposite displacement. The interfaces between domains are topological defects (kinks). Crucially, the electronic subsystem, although isolated, acts as an effective internal bath: the time‑dependent electronic density provides stochastic forces on the lattice, inducing diffusive motion of kinks without any net energy loss. Kinks perform unbiased random walks, annihilate when they meet, and also undergo elastic scattering with a finite probability. This hybrid dynamics is captured by an effective reaction‑diffusion model: \