Simulation of the quantum dynamics of indistinguishable bosons with the method of coupled coherent states

Green, James A.; Shalashilin, Dmitrii V.

doi:10.1103/physreva.100.013607

Cited by 7 publications

(3 citation statements)

References 87 publications

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“…Werther and Grossmann developed a complementary strategy and suggested the procedure of apoptosis which removes quasi-degenerate Gaussian wave packets and thereby circumvents the problem of linear dependency of vibrational coherent states. 239,240 The coupledcoherent states (CCS) method developed by Shalashilin and coworkers 37,[241][242][243] represents nuclear wave function in a basis of trajectory-guided coherent states that are propagated by an averaged quantum potential. The CCS method has been further extended toward multiple coupled potential energy surfaces, resulting in the MCE method, [32][33][34] which represents wave functions by a linear combination of Ehrenfest configurations guided by mean-field trajectories.…”

Section: Davydov Ansätze Versus Other Gaussian Basis-set Methodsmentioning

confidence: 99%

The hierarchy of Davydov's Ansätze and its applications

Zhao

Sun

Chen

et al. 2021

WIREs Comput Mol Sci

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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.

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Section: Davydov Ansätze Versus Other Gaussian Basis-set Methodsmentioning

confidence: 99%

The hierarchy of Davydov's Ansätze and its applications

Zhao

Sun

Chen

et al. 2021

WIREs Comput Mol Sci

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“…ZSs can be viewed as Fermionic Coherent States (CS) of a two-level system. Previously Coherent States of the harmonic oscillator have been used to describe Bosonic systems in second quantisation with the help of Herman-Kluck 17 and Coupled Coherent States propagation methods 18 and also with Generalised Coherent States 19 . Second quantisation Hamiltonians look like those of coupled oscillators with the difference that the oscillators represent the amplitudes and populations of the orbitals occupied by Bosons.…”

Section: Introductionmentioning

confidence: 99%

Electronic energies from coupled fermionic 'Zombie' states imaginary time evolution

Bramley,

Hele,

Shalashilin

2022

Preprint

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Zombie States are a recently introduced formalism to describe coupled coherent Fermionic states which address the Fermionic sign problem in a computationally tractable manner.Previously it has been shown that Zombie States with fractional occupations of spin-orbitals obeyed the correct Fermionic creation and annihilation algebra and presented results for real-time evolution 1 . In this work we extend and build on this formalism by developing efficient algorithms for evaluating the Hamiltonian and other operators between Zombie States and address their normalization. We also show how imaginary time propagation can be used to find the ground state of a system. We also present a biasing method, for setting up a basis set of random Zombie States, that allow much smaller basis sizes to be used while still accurately describing the electronic structure Hamiltonian and its ground state and describe a technique of wave function "cleaning" which removes the contributions of configurations with the wrong number of electrons, improving the accuracy further. We also show how low-lying excited states can be calculated efficiently using a Gram-Schmidt orthogonalization procedure.The proposed algorithm of imaginary time propagation on a biased random grids of Zombie States may present an alternative to existing Quantum Monte Carlo methods.

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“…The fermion coupled coherent states (F-CCS) method was developed to simulate the double ionization of He in intense laser fields [21]. Quite recently, CCS method has been extended to simulate the quantum dynamics of indistinguishable bosons in the second-quantization formalism [22]. A further generalization of the CCS method, the multi-configurational Ehrenfest (MCE) method [23,24], has been proposed to treat nonadiabatic dynamics involving two or several electronic PESs.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a one-dimensional Holstein polaron: The multiconfigurational Ehrenfest method

Chen

Gelin

Shalashilin

2019

The Journal of Chemical Physics

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We have extended the multiconfigurational Ehrenfest (MCE) approach to investigate the dynamics of a one-dimensional Holstein molecular crystal model. It has been shown that the extended MCE approach yields results in perfect agreement with benchmark calculations by the hierarchy equations of motion method. The accuracies of the MCE approach in describing the dynamical properties of the Holstein polaron over a wide range of exciton transfer integral and exciton-phonon coupling are carefully examined by a detailed comparison with the fully variational multiple Davydov D 2 ansatz. It is found that while the MCE approach and the multi-D 2 ansatz produce almost exactly the same results for small transfer integral, the results obtained by the multi-D 2 ansatz start to deviate from those by the MCE approach at longer times for large transfer integral. A large number of coherent state basis functions is required to characterize the delocalized features of the phonon wave function in the case of large transfer integral, which becomes computationally too demanding for the multi-D 2 ansatz. The MCE approach, on the other hand, uses hundreds to thousands of trajectory guided basis functions and converges very well, thus providing an effective tool for accurate, efficient simulation of polaron dynamics.

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Simulation of the quantum dynamics of indistinguishable bosons with the method of coupled coherent states

Cited by 7 publications

References 87 publications

The hierarchy of Davydov's Ansätze and its applications

The hierarchy of Davydov's Ansätze and its applications

Electronic energies from coupled fermionic 'Zombie' states imaginary time evolution

Dynamics of a one-dimensional Holstein polaron: The multiconfigurational Ehrenfest method

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