Polaron dynamics with a multitude of Davydov D$_2$ trial states

TL;DR

This paper introduces a multi-Davydov D$_2$ Ansatz for more accurate simulation of polaron dynamics in molecular crystals, significantly reducing deviation from exact quantum dynamics.

Contribution

The authors develop a multi-D$_2$ Ansatz that extends the traditional Davydov trial states, improving accuracy in modeling exciton-phonon interactions in the Holstein model.

Findings

Multi-D$_2$ Ansatz outperforms single D$_1$ and D$_2$ states in accuracy.

Increasing the number of trial states reduces deviation from Schrödinger dynamics.

The method approaches a numerically exact solution as more trial states are added.

Abstract

We propose an extension to the Davydov D$_2$ Ansatz in the dynamics study of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling using the Dirac-Frenkel time-dependent variational principle. The new trial state by the name of the "multi-D$_2$ Ansatz" is a linear combination of Davydov D$_2$ trial states, and its validity is carefully examined by quantifying how faithfully it follows the Schr\"odinger equation. Considerable improvements in accuracy have been demonstrated in comparison with the usual Davydov trial states, i.e., the single D$_1$ and D$_2$ Ans\"atze. With an increase in the number of the Davydov D$_2$ trial states in the multi-D$_2$ Ansatz, deviation from the exact Schr\"odinger dynamics is gradually diminished, leading to a numerically exact solution to the Schr\"odinger equation.