content_image/429992.jpg content_image/429995.jpg content_image/429996.jpg content_image/429993.jpg content_image/429994.jpg content_image/429991.jpg content_image/430000.jpg content_image/429999.jpg content_image/429998.jpg content_image/429997.jpg
And in this paper, we set 

Solutions to Eq. (A5) and (A6) provide the dynamic in- formation of the exciton-phonon system. 

For the ˜ D trial state, the localized backbone of the translationally-invariant GL Ansatz, we can also derive coupled equation for the time-dependent variational pa- rameters using the Lagrangian formalism 

<img src='content_image/429992.jpg'>

wherein the individual terms can be calculated as follows 

and 

<img src='content_image/429995.jpg'>

with 

<img src='content_image/429996.jpg'>

## Appendix B: The ˜ D trial state 

<img src='content_image/429993.jpg'>

<img src='content_image/429994.jpg'>

<img src='content_image/429991.jpg'>

<img src='content_image/430000.jpg'>

Substituting Eqs. (B1)-(B4) into Eq. (23), one arrives at the equations of time evolution for the ˜ D Ansatz: 

<img src='content_image/429999.jpg'>

<img src='content_image/429998.jpg'>

<img src='content_image/429997.jpg'>

