The hierarchy of Davydov's Ansatze: From guesswork to numerically exact many-body wave functions

This Perspective presents an overview of the development of the hierarchy of Davydov's Ansatze and a few of their applications in many-body problems in computational chemical physics. Davydov's solitons originated in the investigation of vibrational energy transport in proteins in the 1970s. Momentum-space projection of these solitary waves turned up to be accurate variational ground-state wave functions for the extended Holstein molecular crystal model, lending unambiguous evidence to the absence of formal quantum phase transitions in Holstein systems. The multiple Davydov Ansatze have been proposed, with increasing Ansatz multiplicity, as incremental improvements of their single-Ansatz parents. For a given Hamiltonian, the time-dependent variational formalism is utilized to extract accurate dynamic and spectroscopic properties using Davydov's Ansatze as its trial states. A quantity proven to disappear for large multiplicities, the Ansatz relative deviation is introduced to quantify how closely the Schrodinger equation is obeyed. Three finite-temperature extensions to the time-dependent variation scheme are elaborated, i.e., the Monte Carlo importance sampling, the method of thermofield dynamics, and the method of displaced number states. To demonstrate the versatility of the methodology, this Perspective provides applications of Davydov's Ansatze to the generalized Holstein Hamiltonian, variants of the spin-boson model, and systems of cavity-assisted singlet fission, where accurate dynamic and spectroscopic properties of the many-body systems are given by the Davydov trial states.

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This Perspective provides an overview of the development and applications of Davydov's Ansatze in computational chemical physics. The solitons proposed by Davydov in the 1970s have been proven to be accurate variational ground-state wave functions for the Holstein molecular crystal model. Multiple Davydov Ansatze have been proposed as improvements of their single-Ansatz parents. The time-dependent variational formalism is used to extract accurate dynamic and spectroscopic properties using Davydov's Ansatze as trial states.