Real-time evolution of static electron-phonon models in time-dependent electric fields.

Area of Science:

• Condensed Matter Physics
• Quantum Dynamics
• Computational Physics

Background:

• Electron-phonon interactions are fundamental to many condensed matter phenomena.
• Simulating nonequilibrium dynamics in these systems is computationally challenging.
• The adiabatic limit offers a simplified yet relevant regime for study.

Purpose of the Study:

• To develop an exact Monte Carlo method for simulating nonequilibrium electron-phonon dynamics.
• To apply this method to charge-density-wave systems under pulsed electric fields.
• To investigate the response of the Holstein model in one and two dimensions.

Main Methods:

• Exact Monte Carlo simulation in the adiabatic limit (zero phonon frequency).
• Classical sampling of equilibrium phonon distributions.
• Efficient time-dependent evolution of the electronic subsystem in electromagnetic fields.
• Calculation of current, energy, and photoemission spectra.

Main Results:

• The method accurately simulates nonequilibrium dynamics for electron-phonon models.
• Demonstrated utility for charge-density-wave systems in pump-probe scenarios.
• Calculated out-of-equilibrium responses and photoemission spectra for the Holstein model.
• Controlled finite-size effects for system sizes up to 162 sites (1D) and 16x16 lattices (2D).

Conclusions:

• The developed Monte Carlo method provides an exact and efficient tool for studying nonequilibrium electron-phonon dynamics.
• This approach is particularly valuable for understanding phenomena like charge-density waves under external fields.
• The findings offer insights into experimental techniques such as pump-probe spectroscopy.