Fast, Accurate Simulation of Polaron Dynamics and Multidimensional Spectroscopy by Multiple Davydov Trial States

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 D1 (D2) ansatz, referred to as the "multi-D1 ansatz" ("multi-D2 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, 2D spectra have been calculated for systems with off-diagonal exciton-phonon coupling by employing the multiple D2 ansatz to compute the nonlinear response function, testifying to the great potential of the multiple D2 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 multipeak structure appears for strong off-diagonal coupling.

Benchmarking the stochastic time-dependent variational approach for excitation dynamics in molecular aggregates

“…While finite temperature was included in calculations of Refs. [63,42,43], that was done via a secondary bath, that was not treated on equal footing with the primary bath. The sTDVA, introduced in Ref.…”

“…In Refs. [46,39,63,42,43] it was assumed that the phonons couple to each site non-locally. Therefore, the site energy fluctuations were totally correlated, and no incoherent energy transfer was possible.…”

“…it must be possible to find a generalized probability distribution for the thermal state in the basis constructed with the Ansatz functions. It was recently shown that for a molecular crystal model, the usage of the D 2 Ansatz with higher multiplicity greatly increased the accuracy of solution in the zero temperature case [43]. The multi-D 1 Ansatz applied to the traditional spinboson model was shown to improve numerical accuracy by a large factor [68], and a generalized coherent state Ansatz provides similarly accurate results in zero-temperature case for a model excitonic polaron system [69].…”

Transient Dynamics of Super Bloch Oscillations of a 1D Holstein Polaron under the Influence of an External AC Electric Field

“…The multiple Davydov trial states with a multiplicity M , which are essentially M copies of the corresponding single Davydov Ansatz , have been developed to investigate the time evolution of the Holstein polaron following the Dirac–Frenkel variational principle . A series of multiple Davydov trial states, that is, the multiple Davydov D 1 , D 1.5 , and D 2 Ansätze , have been proposed, demonstrating significant improvements over single Davydov states in the flexibility and the accuracy of the trial states . Recently, the multiple Davydov D 2 trial state, also known as the multi‐D 2 Ansatz , has been successfully applied to obtain accurate dynamics of a variety of open quantum systems, including the singlet fission model and the dissipative Landau–Zener model …”

Dynamics of coherence, localization and excitation transfer in disordered nanorings

“…The accuracy of the variational Davydov wave function has been extensively analyzed in the past [90,91] and multiple Davydov trial states have been recently proved to provide [32,92] accurate results comparable with numerically exact methods such as HEOM. The addition of static disorder does not impact the performance of the variational formalism in any noticeable way and the reader is referred to Ref.…”