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We study the Holstein model of spinless fermions, which at half-fillingexhibits a quantum phase transition from a metallic Tomonaga-Luttinger liquidphase to an insulating charge-density-wave (CDW) phase at a criticalelectron-phonon coupling strength. In our work, we focus on the real-timeevolution starting from two different types of initial states that are CDWordered: (i) ideal CDW states with and without additional phonons in the systemand (ii) correlated ground states in the CDW phase. We identify the mechanismfor CDW melting in the ensuing real-time dynamics and show that it stronglydepends on the type of initial state. We focus on the far-from-equilibriumregime and emphasize the role of electron-phonon coupling rather than dominantelectronic correlations, thus complementing a previous study of photo-inducedCDW melting [H. Hashimoto and S. Ishihara, Phys. Rev. B 96, 035154 (2017)]. Thenumerical simulations are performed by means of matrix-product-state basedmethods with a local basis optimization (LBO). Within these techniques, onerotates the local (bosonic) Hilbert spaces adaptively into an optimized basisthat can then be truncated while still maintaining a high precision. In thiswork, we extend the time-evolving block decimation (TEBD) algorithm with LBO,previously applied to single-polaron dynamics, to a half-filled system. Wedemonstrate that in some parameter regimes, a conventional TEBD method withoutLBO would fail. Furthermore, we introduce and use a ground-state density-matrixrenormalization group method for electron-phonon systems using local basisoptimization. In our examples, we account for up to $M_{\rm ph} = 40$ barephonons per site by working with $O(10)$ optimal phonon modes.

Charge-density-wave melting in the one-dimensional Holstein model