Pseudospin Formulation of Quench Dynamics in the Semiclassical Holstein Model

TL;DR

This paper introduces a pseudospin approach to study the nonequilibrium dynamics of charge-density-wave order in the Holstein model, revealing persistent oscillations due to lattice feedback and distinguishing electron-lattice effects from purely electronic behavior.

Contribution

It develops a pseudospin formulation for the Holstein model's quench dynamics, highlighting the impact of lattice degrees of freedom on long-term behavior and oscillation persistence.

Findings

Persistent CDW oscillations due to lattice feedback

Distinct dynamical regimes analogous to superconductors

Lattice dynamics crucially influence nonequilibrium behavior

Abstract

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.