Holstein polaron transport from numerically "exact" real-time quantum dynamics simulations

Abstract

Numerically "exact" methods addressing the dynamics of coupled electron--phonon systems have been intensively developed. Nevertheless, the corresponding results for the electron mobility ${\mu }_{\mathrm{dc}}$ are scarce, even for the one-dimensional (1d) Holstein model. Building on our recent progress on single-particle properties, here, we develop the momentum-space hierarchical equations of motion (HEOM) method to evaluate real-time two-particle correlation functions of the 1d Holstein model at finite temperature. We compute numerically "exact" dynamics of the current--current correlation function up to real times sufficiently long to capture the electron's diffusive motion and provide reliable results for ${\mu }_{\mathrm{dc}}$ in a wide range of model parameters. In contrast to the smooth ballistic-to-diffusive crossover in the weak-coupling regime, we observe a temporally limited slow-down of the electron on intermediate time scales already in the intermediate-coupling regime, which translates to a finite-frequency peak in the optical response. Our momentum-space formulation lowers the numerical effort with respect to existing HEOM-method implementations, while we remove the numerical instabilities inherent to the undamped-mode HEOM by devising an appropriate hierarchy closing scheme. Still, our HEOM remains unstable at too low temperatures, for too strong electron--phonon coupling, and for too fast phonons.

final, published version; main text: 23 pages, 8 figures; supplementary material contains detailed information on the dataset available at https://doi.org/10.5281/zenodo.8068546

References in corpus (13)

• Perspective: Numerically "exact" approach to open quantum dynamics: The hierarchical equations of motion (HEOM)
• Reduced hierarchical equations of motion in real and imaginary time: Correlated initial states and thermodynamic quantities
• Dynamics of quantum dissipation systems interacting with bosonic canonical bath: Hierarchical equations of motion approach
• Green's function of a dressed particle
• The Green's Function of the Holstein Polaron
• Removing instabilities in the hierarchical equations of motion: exact and approximate projection approaches
• Non-Markovian quantum state diffusion for absorption spectra of molecular aggregates
• Transport properties of the one-dimensional Hubbard model at finite temperature
• On the Munn-Silbey approach to polaron transport with off-diagonal coupling
• Crossover from Super- to Sub-Diffusive Motion and Memory Effects in Crystalline Organic Semiconductors
• Optical absorption and activated transport in polaronic systems
• A simple improved low temperature correction for the hierarchical equations of motion
• Dynamics of coherence, localization and excitation transfer in disordered nanorings

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• Charge transport limited by nonlocal electron-phonon interaction. I. Hierarchical equations of motion approach
• Dynamical quantum typicality: Simple method for investigating transport properties applied to the Holstein model
• Identification of the transport regimes of the one-dimensional Holstein model
• Numerically "exact" charge transport dynamics in a dissipative electron-phonon model rationalizing the success of the transient localization scenario
• Beyond-quasiparticle transport with vertex correction: self-consistent ladder formalism for electron-phonon interactions
• Quantum-classical study of charge transport in organic semiconductors with multiple low-frequency vibrational modes
• Applicability of the cumulant expansion method for the calculation of transport properties in electron-phonon systems
• Testing bath correlation functions for open quantum dynamics simulations