The hierarchy of Davydov's Ansätze and its applications

Abstract

This review provides a bird's eye view over the development of the hierarchy of Davydov's Ansätze and its applications in a variety of problems in computational physical chemistry. Davydov's original solitons appeared in the 1970s as a candidate for vibrational energy carriers in proteins, thanks to their association with the Fröhlich Hamiltonian and the Holstein molecular crystal model.Momentum-space projection of those solitary waves emerged to be great approximations to the ground-state wave functions of the extended Holstein Hamiltonian, lending unambiguous evidence to the absence of formal quantum phase transitions in those systems. The multiple Davydov Ansätze are introduced, with increasing multiplicity, as incremental improvements of their corresponding single-Ansatz parents. The time-dependent variational formalism of Davydov's Ansätze is discussed in great detail, and the relative deviation of the Ansätze is constructed to quantify how faithfully they follow the Schrödinger equation, a quantity that is shown to vanish in the limit of large multiplicities. Three approaches to finite-temperature variational dynamics of Davydov's Ansätze are demonstrated, namely, the Monte Carlo importance sampling, the method of thermo-field dynamics, and the method of displaced number states. Applications of Davydov's Ansätze are given to variants of the spin-boson model, the Landau-Zener transition, the Holstein Hamiltonian, energy transfer in light-harvesting, and singlet fission in organic photovoltaics.As an example, simulation of multidimensional spectroscopic signals via Davydov's Ansätze is fully implemented for the finite-temperature fission process in crystalline rubrene.

Modeling molecular J and H aggregates using multiple-Davydov D2 ansatz

“…The mD 2 Ansatz and, its more complex variant, mD 1 Ansatz 14 have been applied to study polaron dynamics in Holstein molecular crystals, 13 the spin-boson models 15 and for nonadiabatic dynamics of single molecules, 6,16 as well as to simulate nonlinear response function of molecular aggregates 7,13 and others. [17][18][19][20] A more in-depth overview of the various types of Davydov Ansatze and their applications can be found in a recent review article by Zhao et al 21 However, a well-defined strategy to determine the required number of multiples in mD 2 Ansatz (or the depth) needed to obtain the converged result is lacking. The absorption spectrum and excitation relaxation dynamics of a linear molecular aggregate are key quantities that may serve for establishing the relationship between model parameters and the parameters of the Ansatz.…”

“…The mD 2 Ansatz and, its more complex variant, mD 1 Ansatz 14 have been applied to study polaron dynamics in Holstein molecular crystals, 13 the spin-boson models 15 and for nonadiabatic dynamics of single molecules, 6,16 as well as to simulate nonlinear response function of molecular aggregates 7,13 and others. 17–20 A more in-depth overview of the various types of Davydov Ansatze and their applications can be found in a recent review article by Zhao et al 21…”

Engineering Cavity Singlet Fission in Rubrene

“…In the past decade, the hierarchy of multiple Davydov ansätze has been successfully applied in a variety of quantum many-body problems such as Landau–Zener transitions, − SF dynamics and related spectroscopy, , and polariton dynamics in a microcavity . In this work, we adopt a time-dependent variant of the multiple Davydov ansätze − to systematically investigate the polaritonic dynamics of the CI-driven non-adiabatic process in crystalline rubrene. A highly adaptable wave-function-based method, the multiple Davydov ansätze offer an alternative to the density matrix formalism for computing wave function evolution at zero or finite temperature. , In particular, the multiple Davydov D 2 (multi-D 2 ) ansatz has been utilized to uncover high-precision dynamics of the Holstein–Tavis–Cummings (HTC) model, which results in fast, accurate simulation of multidimensional spectroscopic signals .…”

“…In this work, we adopt a time-dependent variant of the multiple Davydov ansätze − to systematically investigate the polaritonic dynamics of the CI-driven non-adiabatic process in crystalline rubrene. A highly adaptable wave-function-based method, the multiple Davydov ansätze offer an alternative to the density matrix formalism for computing wave function evolution at zero or finite temperature. , In particular, the multiple Davydov D 2 (multi-D 2 ) ansatz has been utilized to uncover high-precision dynamics of the Holstein–Tavis–Cummings (HTC) model, which results in fast, accurate simulation of multidimensional spectroscopic signals . In the absence of the rotating-wave approximation (RWA), the photon mode should be treated on an equal footing with the phonon modes, a requirement that can be easily accommodated in the method of the multi-D 2 ansatz.…”

“…The multi-D 2 ansatz belongs to a large family of methods that employ time-dependent Gaussian basis functions to accurately solve multidimensional time-dependent Schrödinger equations. This method has the advantages of numerical accuracy and high efficiency, which have been extensively verified in describing the states of various many-body systems . We can construct the multi-D 2 ansatz with multiplicity M as a superposition of M copies of the single Davydov D 2 ansatz, that is, In eq , | i ⟩ is the i th global electronic state of the molecular system.…”