The hierarchy of Davydov's Ansaetze and its applications

• Main Authors: Zhao, Yang, Sun, Kewei, Chen, Lipeng, Gelin, Maxim
• Other Authors: School of Materials Science and Engineering
• Format: Article
• Language: English
• Published: 2023
• Subjects: Science::Chemistry; Science::Chemistry::Physical chemistry; Davydov's Ansatz; Holstein Polaron; Spin-Boson Model; Singlet Fission; Light Harvesting; Landau-Zener Transitions
• Online Access: https://hdl.handle.net/10356/165189
• Institution: Nanyang Technological University

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 computa- tional physical chemistry. Davydov's original solitons appeared in the 1970s as a candidate for vibrational energy carriers in proteins, thanks to their associa- tion 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 quan- tum 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 formal- ism 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 pro- cess in crystalline rubrene.