# Polaron dynamics with off-diagonal coupling: beyond the Ehrenfest approximation

## TL;DR

This paper advances the simulation of exciton-phonon dynamics in molecular crystals by employing a variational method with the multi-D2 Ansatz, surpassing the Ehrenfest approximation in accuracy and capturing detailed exciton momentum and temperature effects.

## Contribution

The study introduces a multi-D2 variational approach that improves upon the Ehrenfest approximation for modeling off-diagonal exciton-phonon coupling dynamics.

## Key findings

- Multi-D2 Ansatz yields more accurate exciton momentum distributions.
- Exciton steady-state distributions depend on transfer integral and off-diagonal coupling.
- The variational method is effective across temperature regimes.

## Abstract

Treated traditionally by the Ehrenfest approximation, dynamics of a one-dimensional molecular crystal model with off-diagonal exciton-phonon coupling is investigated in this work using the Dirac-Frenkel time-dependent variational principle with the multi-D$_2$ {\it Ansatz}. It is shown that the Ehrenfest method is equivalent to our variational method with the single D$_2$ {\it Ansatz}, and with the multi-D$_2$ {\it Ansatz}, the accuracy of our simulated dynamics is significantly enhanced in comparison with the semi-classical Ehrenfest dynamics. The multi-D$_2$ {\it Ansatz} is able to capture numerically accurate exciton momentum probability and help clarify the relation between the exciton momentum redistribution and the exciton energy relaxation. The results demonstrate that the exciton momentum distributions in the steady state are determined by a combination of the transfer integral and the off-diagonal coupling strength, independent of the excitonic initial conditions. We also probe the effect of the transfer integral and the off-diagonal coupling on exciton transport in both real and reciprocal space representations. Finally, the variational method with importance sampling is employed to investigate temperature effects on exciton transport using the multi-$\rm D_2$ {\it Ansatz}, and it is demonstrated that the variational approach is valid in both low and high temperature regimes.