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

TL;DR

This paper introduces an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon systems under time-dependent electric fields, focusing on charge-density-wave materials in the adiabatic limit.

Contribution

The authors develop a novel Monte Carlo approach for real-time simulation of electron-phonon models in the zero phonon frequency limit, enabling efficient analysis of out-of-equilibrium responses.

Findings

Successfully simulated current and energy response after electric pulses.

Calculated photoemission spectra before and after pumping.

Controlled finite-size effects in large systems.

Abstract

We present an exact Monte Carlo method to simulate the nonequilibrium dynamics of electron-phonon models in the adiabatic limit of zero phonon frequency. The classical nature of the phonons allows us to sample the equilibrium phonon distribution and efficiently evolve the electronic subsystem in a time-dependent electromagnetic field for each phonon configuration. We demonstrate that our approach is particularly useful for charge-density-wave systems experiencing pulsed electric fields, as they appear in pump-probe experiments. For the half-filled Holstein model in one and two dimensions, we calculate the out-of-equilibrium response of the current and the energy after a pulse is applied as well as the photoemission spectrum before and after the pump. Finite-size effects are under control for chains of $162$ sites (in one dimension) or $16\times 16$ square lattices (in two dimensions).