Stochastic semiclassical theory for non-equilibrium electron-phonon coupled systems

TL;DR

This paper introduces a stochastic semiclassical method within non-equilibrium dynamical mean-field theory to model coupled electron-phonon systems, capturing electronic fluctuations beyond traditional approaches for better understanding photo-induced phase transitions.

Contribution

The paper presents a novel stochastic semiclassical framework that self-consistently incorporates electronic fluctuations into phonon dynamics in non-equilibrium electron-lattice models.

Findings

Good agreement with quantum Monte Carlo data for phonon distributions.

Effective modeling of electron-phonon coupled dynamics during phase transitions.

Framework extendable to more complex multi-orbital and interacting systems.

Abstract

We discuss a semiclassical approach to solve the quantum impurity model within non-equilibrium dynamical mean-field theory for electron-lattice models. The effect of electronic fluctuations on the phonon is kept beyond Ehrenfest dynamics, leading to a stochastic phonon evolution with damping and noise terms that are self-consistently determined by the electronic correlation functions in the fluctuating phonon field. Together with a solution of the electronic model based on a non-perturbative quantum Boltzmann equation, the approach can be used to address the coupled dynamics of the electrons and the lattice during photo-induced phase transitions. Results for the Anderson-Holstein model are benchmarked against numerically exact quantum Monte Carlo data. We find good agreement for the phonon distribution function at temperatures comparable to the charge ordering temperature. The general formulation can be extended to models with electron-electron interactions or multi-orbital systems.