Fast, accurate simulation of polaron dynamics and multidimensional spectroscopy by multiple Davydov trial states

TL;DR

This paper introduces a highly accurate and efficient variational approach using multiple Davydov trial states to simulate polaron dynamics and multidimensional spectroscopy in molecular crystals, including novel 2D spectra calculations.

Contribution

The study develops and validates a multi-Davydov Ansatz method for simulating complex quantum dynamics and spectra with improved accuracy and efficiency over existing techniques.

Findings

Multi-Davydov Ansatz accurately reproduces exciton dynamics.

First calculation of 2D spectra with off-diagonal exciton-phonon coupling.

Identified spectral features varying with coupling strength.

Abstract

By employing the Dirac-Frenkel time-dependent variational principle, we study the dynamical properties of the Holstein molecular crystal model with diagonal and off-diagonal exciton-phonon coupling. A linear combination of the Davydov D$_1$ (D$_2$) Anstaz, referred to as the multi-D$_1$ Ansatz (multi-D$_2$ Ansatz), is used as the trial state with enhanced accuracy but without sacrificing efficiency. The time evolution of the exciton probability is found to be in perfect agreement with that of the hierarchy equations of motion, demonstrating the promise the multiple Davydov trial states hold as an efficient, robust description of dynamics of complex quantum systems. In addition to the linear absorption spectra computed for both diagonal and off-diagonal cases, for the first time, $2$D spectra have been calculated for systems with off-diagonal exciton-phonon coupling by employing the multiple $D_2$ Ansatz to compute the nonlinear response function, testifying to the great potential of the multiple $D_2$ Ansatz for fast, accurate implementation of multidimensional spectroscopy. It is found that the signal exhibits a single peak for weak off-diagonal coupling, while a vibronic multi-peak structure appears for strong off-diagonal coupling.