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

Abstract

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 photo-induced 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 $M_{\mathrm{ph}}=40$ bare phonons per site by working with $O(10)$ optimal phonon modes.

20 pages, 18 figures, data for all plots in the form of .txt files can be found in the auxiliary files

References in corpus (28)

• The density-matrix renormalization group in the age of matrix product states
• Relaxation of antiferromagnetic order in spin-1/2 chains following a quantum quench
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• Green's function of a dressed particle
• Dynamics of photoinduced Charge Density Wave-metal phase transition in K0.3MoO3
• The Green's Function of the Holstein Polaron
• Snapshots of the retarded interaction of charge carriers with ultrafast fluctuations in cuprates
• Photo-induced states in a Mott insulator
• Quantum Monte Carlo and variational approaches to the Holstein model
• Photo-induced enhancement of excitonic order
• Nonthermal symmetry broken states in the strongly interacting Hubbard model
• Relaxation dynamics of the Holstein polaron
• Nonequilibrium dynamics of the Holstein polaron driven by external electric field
• Systematic improvement of the Momentum Average approximation for the Green's function of a Holstein polaron
• Real-time decay of a highly excited charge carrier in the one-dimensional Holstein model
• Field-induced polaron formation in the Holstein-Hubbard model
• Simulating generic spin-boson models with matrix product states
• Ground state properties of the Holstein model near the adiabatic limit
• Anatomy of quantum critical wave functions in dissipative impurity problems
• Two-bath spin-boson model: Phase diagram and critical properties
• Photoinduced in-gap excitations in the one-dimensional extended Hubbard model
• Density matrix renormalization group approach of the spin-boson model
• Localization of Large Polarons in the Disordered Holstein Model
• Coexistence of excited polarons and metastable delocalized states in photo-induced metals
• Phase diagram of the Holstein polaron in one dimension
• Emergence of states in the phonon spectral function of the Holstein polaron below and above the one-phonon continuum
• Continuous-time quantum Monte Carlo for fermion-boson lattice models: Improved bosonic estimators and application to the Holstein model
• Scattering of an electronic wave packet by a one-dimensional electron-phonon-coupled structure