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arXiv:2406.11755

Photo-induced pattern formations and melting of charge-density-wave order

Yang, Lingyu, Gia-Wei Chern

Published Jun 17, 2024• 0 citations
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Abstract

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.

DOI
10.48550/arxiv.2406.11755

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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.
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 study postquench dynamics of charge density wave (CDW) order in the square-lattice $t\text{\ensuremath{-}}V$ model. The ground state of this system at half-filling is characterized by a checkerboard modulation of particle density. A generalized self-consistent mean-field method, based on the time-dependent variational principle, is employed to describe the dynamical evolution of the CDW states. Assuming a homogeneous CDW order throughout the quench process, the time-dependent mean-field approach is reduced to the Anderson pseudospin method. Quench simulations based on the Bloch equation for pseudospins produce three canonical behaviors of order-parameter dynamics: phase-locked persistent oscillation, Landau-damped oscillation, and dynamical vanishing of the CDW order. We further develop an efficient real-space von Neumann equation method to incorporate dynamical inhomogeneity into simulations of quantum quenches. Our large-scale simulations uncover complex pattern formations in the postquench CDW states, especially in the strong quench regime. The emergent spatial textures are characterized by super density modulations on top of the short-period checkerboard CDW order. Our demonstration of pattern formation in quenched CDW states, described by a simple broken Z2{Z}_{2}Z2​ symmetry, underscores the importance of dynamical inhomogeneity in quantum quenches of many-body systems with more complex orders.
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 study the Holstein model of spinless fermions, which at half filling exhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquid phase to an insulating charge-density-wave (CDW) phase at a critical electron-phonon coupling strength. In our work, we focus on the real-time evolution starting from two different types of initial states that are CDW ordered: (i) ideal CDW states with and without additional phonons in the system and (ii) correlated ground states in the CDW phase. We identify the mechanism for CDW melting in the ensuing real-time dynamics and show that it strongly depends on the type of initial state. We focus on the far-from-equilibrium regime and emphasize the role of electron-phonon coupling rather than dominant electronic correlations, thus complementing a previous study of photoinduced CDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. The numerical simulations are performed by means of matrix-product-state based methods with a local basis optimization (LBO). Within these techniques, one rotates the local (bosonic) Hilbert spaces adaptively into an optimized basis that can then be truncated while still maintaining a high precision. In this work, we extend the time-evolving block decimation (TEBD) algorithm with LBO, previously applied to single-polaron dynamics, to a half-filled system. We demonstrate that in some parameter regimes, a conventional TEBD method without LBO would fail. Furthermore, we introduce and use a ground-state density-matrix renormalization group method for electron-phonon systems using local basis optimization. In our examples, we account for up to Mph=40{M}_{\mathrm{ph}}=40Mph​=40 bare phonons per site by working with O(10)O(10)O(10) optimal phonon modes.
We use infinite matrix-product-state techniques to study the time evolution of the charge-density-wave (CDW) order after a quench or a light pulse in a fundamental fermion-boson model. The motion of fermions in the model is linked to the creation of bosonic excitations, which counteracts the melting of the CDW order. For low-energy quenches corresponding to a change of the boson relaxation rate, we find behavior similar to that in an effective t−V model. When the boson energy is quenched instead or a light pulse is applied to the system, the transient dynamics are more complex, with the CDW order first quickly decreasing to an intermediate value while the density-wave-like order of the bosons rises. In the case of pulse irradiation, the subsequent time evolution of the CDW order depends strongly on the photon frequency. For frequencies slightly below the boson energy, we observe a temporary increase of the CDW order parameter. Our results reveal the complex physics of driven Mott insulators in low-dimensional systems with strong correlations. Published by the American Physical Society 2024
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∼t−1/3n \sim t^{-1/3}n∼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.