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arXiv:2602.05815

Suppressed coarsening after an interaction quench in the Holstein chain

Ho Jang, Gia-Wei Chern

Published Feb 5, 2026• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2602.05815

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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.
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We present a pseudospin formulation for the post-quench dynamics of charge-density-wave (CDW) order in the half-filled spinless Holstein model on a square lattice, assuming spatially homogeneous evolution. This Anderson pseudospin description captures the coherent nonequilibrium dynamics of the coupled electron-lattice system. Numerical simulations reveal three distinct dynamical regimes of the CDW order parameter following a quench-locked oscillations, Landau-damped dynamics, and overdamped relaxation-closely paralleling quench dynamics in BCS superconductors and other electronically driven symmetry-breaking phases. Crucially, however, the presence of dynamical lattice degrees of freedom leads to qualitatively different long-time behavior. In particular, while the oscillation amplitude is reduced in the damped regimes, CDW oscillations do not fully decay but instead persist indefinitely due to feedback from the lattice field. We further show that these persistent oscillations are characterized by a nonequilibrium electronic distribution, which provides an intuitive understanding of both their amplitude and the renormalization of the oscillation frequency relative to the bare Holstein phonon frequency. Our results highlight the essential role of lattice dynamics in nonequilibrium ordered phases and establish a clear distinction between electron-lattice-driven CDW dynamics and their purely electronic counterparts.
We investigate the out-of-equilibrium dynamics of a photoexcited charge-density-wave (CDW) state in the square-lattice Holstein model, in a setup similar to a pump-probe experiment. At half-filling, the ground state of this system is characterized by a checkerboard modulation of particle densities, accompanied by a concomitant lattice distortion. An efficient real-space dynamics method integrating the von Neumann equation for electron density matrix and Newton equation for classical lattice dynamics is developed to simulate the dynamical evolution of a photoexcited Holstein system. We find that the energy injected by a short pump pulse results in the reduction of the CDW order and the generation of coherent phonons. At strong photoexcitations, while the CDW order is melted in the sense that the time-averaged order parameter vanishes, a dynamical CDW state is self-sustained by the strong coherent phonon oscillations. Our large-scale simulations further uncover a dynamical regime of intermediate fluence where complex pattern formation is induced by the pump pulse. The emergent spatial textures are characterized by super density modulations on top of the short-range checkerboard CDW order. Our demonstration of pattern formation highlights the significance of dynamical inhomogeneity in quantum many-body systems in pump-probe experiments.
We investigate the out-of-equilibrium dynamics of a photo-excited charge-density-wave (CDW) state in the square-lattice Holstein model, in a setup similar to a pump-probe experiment. At half-filling, the ground state of this system is characterized by a checkerboard modulation of particle densities, accompanied by a concomitant lattice distortion. An efficient real-space dynamics method integrating the von~Neumann equation for electron density matrix and Newton equation for classical lattice dynamics is developed to simulate the dynamical evolution of a photo-excited Holstein system. We find that the energy injected by a short pump pulse results in the reduction of the CDW order and the generation of coherent phonons. At strong photoexcitations, while the CDW order is melted in the sense that the time-averaged order parameter vanishes, a dynamical CDW state is self-sustained by the strong coherent phonon oscillations. Our large-scale simulations further uncover a dynamical regime of intermediate fluence where complex pattern formation is induced by the pump pulse. The emergent spatial textures are characterized by super density modulations on top of the short-range checkerboard CDW order. Our demonstration of pattern formation highlights the significance of dynamical inhomogeneity in quantum many-body systems in pump-probe experiments.
Charge-density wave phases in quantum materials stem from the complex interplay of electronic and lattice degrees of freedom. Nowadays, various time-resolved spectroscopy techniques allow to actively manipulate such phases and monitor their dynamics in real time. Modeling such nonequilibrium dynamics theoretically is a great challenge and exact methods can usually only treat a small number of atoms and finitely many phonons. We approach the melting of charge-density waves in a Holstein model after a sudden switch-on of the electronic hopping from two perspectives. We prove that in the noninteracting and in the strong-coupling limit, the CDW order parameter on high-dimensional hypercubic lattices obeys a factorization relation for long times, such that its dynamics can be reduced to the one-dimensional case. Secondly, we present numerical results from semiclassical techniques based on the truncated Wigner approximation for two spatial dimensions. A comparison with exact data obtained for a Holstein chain shows that a semiclassical treatment of both the electrons and phonons is required in order to correctly describe the phononic dynamics. This is confirmed, in addition, for a quench in the electron-phonon coupling strength.