Abstract
We investigate the post-quench dynamics of charge-density-wave (CDW) order in the square-lattice $t$-$V$ model and Holstein model. Both systems exhibit a ground state characterized by a checkerboard modulation of electron density at half-filling. In the $t$-$V$ model, we employ a generalized self-consistent mean-field method, based on the time-dependent variational principle, to describe the dynamical evolution of CDW states. By assuming a homogeneous CDW order throughout the quench process, this approach reduces to the Anderson pseudospin method. Quench simulations using the Bloch equation for pseudospins reveal three canonical behaviors of order-parameter dynamics: phase-locked persistent oscillation, Landau-damped oscillation, and dynamical vanishing of the CDW order.
To incorporate dynamical inhomogeneity into quench simulations, we develop an efficient real-space von Neumann equation method. Large-scale simulations uncover complex pattern formations in post-quench CDW states, particularly in the strong quench regime. These emergent spatial textures are characterized by super density modulations atop the short-period checkerboard CDW order, highlighting the significance of dynamical inhomogeneity in quantum quenches of many-body systems with broken $Z_2$ symmetry.
In addition, we address artifacts in time evolution introduced by the time-dependent mean-field theory by studying the non-adiabatic post-quench dynamics of CDW states in the Holstein model, which is numerically exact when lattice degrees of freedom are treated classically. We derive the Anderson pseudospin formulation and Newtonian equations of motion for the electronic and lattice degrees of freedom, respectively, to describe the dynamical evolution of CDW states and lattice distortions. Quench simulations reveal three canonical behaviors of order-parameter and lattice dynamics, consistent with those observed in the $t$-$V$ model.
Real-space simulations in the Holstein model explore two post-quench scenarios. In the first, the initial state is prepared with vanishing electron-lattice coupling, and quenching the coupling constant induces the formation of CDW domains, resulting in either anomalous coarsening or spontaneous glassy states depending on the final coupling constant. In the second scenario, starting from a checkerboard modulation of charge density, quenching to a different finite coupling constant results in spatial inhomogeneity that satisfies parametric instability. The rich physics observed in the post-quench dynamics of CDW states in the Holstein model arises from the interplay between electronic and lattice degrees of freedom.
Finally, we investigate the out-of-equilibrium dynamics of a photo-excited CDW state in the square-lattice Holstein model, similar to the setup in a pump-probe experiment. Our extensive simulations show that the energy injected by a short pump pulse results in the reduction of the CDW order and the generation of coherent phonons. For a pump pulse with a large fluence or a center frequency greater than the CDW bandgap, the photoexcitation leads to a complete melting of the CDW order. Furthermore, our simulations reveal a dynamical regime at intermediate fluence where the pump pulse induces complex pattern formation. These emergent spatial textures are characterized by super density modulations on top of the short-range checkerboard CDW order. Our findings highlight the significance of dynamical inhomogeneity in quantum many-body systems subjected to pump-probe experiments.
