Real-time non-adiabatic dynamics in the one-dimensional Holstein model: Trajectory-based vs exact methods.

Area of Science:

• Condensed matter physics
• Quantum chemistry
• Computational physics

Background:

• The Holstein model is a key theoretical tool for studying electron-phonon interactions.
• Accurate real-time dynamics simulations are crucial for understanding quantum systems.
• Existing quantum chemistry methods have limitations in describing complex dynamics.

Purpose of the Study:

• To benchmark various quantum chemistry dynamics methods against exact quantum many-body techniques.
• To evaluate the performance of multitrajectory Ehrenfest, fewest-switches surface-hopping, and multiconfigurational Ehrenfest methods.
• To assess the accuracy of these methods for the Holstein model across different system sizes and initial conditions.

Main Methods:

• Benchmarking quantum chemistry methods (multitrajectory Ehrenfest, surface-hopping, multiconfigurational Ehrenfest) against exact quantum many-body techniques.
• Studying the Holstein model, a paradigmatic model for electron-phonon coupling.
• Utilizing time-dependent density matrix renormalization group with local basis optimization (DMRG-LBO) for exact dynamics in extended systems.

Main Results:

• Multitrajectory Ehrenfest accurately captures only ultrashort time dynamics.
• Surface-hopping methods offer better long-time accuracy but struggle with short-time coherences.
• Multiconfigurational Ehrenfest significantly improves upon multitrajectory Ehrenfest and converges to exact results for small systems.

Conclusions:

• Multiconfigurational Ehrenfest is a promising method for simulating quantum dynamics, with convergence dependent on the number of configurations for extended systems.
• DMRG-LBO serves as a valuable benchmark for assessing the accuracy of quantum chemistry dynamics methods.
• The study provides insights into the strengths and weaknesses of different quantum dynamics simulation techniques for condensed matter models.