Development of a pure diffusion quantum Monte Carlo method using a full generalized Feynman–Kac formula. I. Formalism

Caffarel, Michel; Claverie, P.

doi:10.1063/1.454227

Cited by 112 publications

(85 citation statements)

References 30 publications

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“…and the corresponding modification in the Feynman-Kac functional [33,34]. But it is clear that changing the process according to (2.9) only relabels the state space.…”

Section: The Feynman-kac Functional For Distinguishable Particlesmentioning

confidence: 99%

Many-body diffusion and path integrals for identical particles

1996

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For distinguishable particles it is well known that Brownian motion and a Feynman-Kac functional can be used to calculate the path integral (for imaginary times) for a general class of scalar potentials. In order to treat identical particles, we exploit the fact that this method separates the problem of the potential, dealt with by the Feynman-Kac functional, from the process which gives sample paths of a non-interacting system. For motion in 1 dimension, we emphasize that the permutation symmetry of the identical particles completely determines the domain of Brownian motion and the appropriate boundary conditions: absorption for fermions, reflection for bosons. Further analysis of the sample paths for motion in 3 dimensions allows us to decompose these paths into a superposition of 1-dimensional sample paths. This reduction expresses the propagator (and consequently the energy and other thermodynamical quantities) in terms of well-behaved 1-dimensional fermion and boson diffusion processes and the Feynman-Kac functional.

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“…and the corresponding modification in the Feynman-Kac functional [33,34]. But it is clear that changing the process according to (2.9) only relabels the state space.…”

Section: The Feynman-kac Functional For Distinguishable Particlesmentioning

confidence: 99%

Many-body diffusion and path integrals for identical particles

1996

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“…[18] Of course, a similar formula can also be obtained in a DMC scheme. [17] Now, using formula (60) we get…”

Section: Beyond Variational Monte Carlomentioning

confidence: 97%

“…(52), by expressing the unknown quantity ψ 0 ′ ψ 0 as a computable stochastic average. Choosing a λ-independent trial wave function ψ T we can write [34,35,18] …”

Section: Beyond Variational Monte Carlomentioning

confidence: 99%

“…A second possible strategy to cope with the systematic error is to perform an "exact" QMC calculation based on one of the variants of the so-called "Forward Walking" scheme. [17][18][19] Unfortunately, such schemes are known to be intrinsically unstable and, therefore, very time consuming. In practice, the possibility of getting or not a satisfactory answer depends very much on the accuracy required and on the type of observable considered.…”

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confidence: 99%

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Zero-variance zero-bias principle for observables in quantum Monte Carlo: Application to forces

Assaraf

Caffarel

2003

The Journal of Chemical Physics

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112

114

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A simple and stable method for computing accurate expectation values of observable with Variational Monte Carlo (VMC) or Diffusion Monte Carlo (DMC) algorithms is presented. The basic idea consists in replacing the usual "bare" estimator associated with the observable by an improved or "renormalized" estimator. Using this estimator more accurate averages are obtained: Not only the statistical fluctuations are reduced but also the systematic error (bias) associated with the approximate VMC or (fixed-node) DMC probability densities. It is shown that improved estimators obey a Zero-Variance ZeroBias (ZVZB) property similar to the usual Zero-Variance Zero-Bias property of the energy with the local energy as improved estimator. Using this property improved estimators can be optimized and the resulting accuracy on expectation values may reach the remarkable accuracy obtained for total energies. As an important example, we present the application of our formalism to the computation of forces in molecular systems. Calculations of the entire force curve of the H 2 ,LiH, and Li 2 molecules are presented. Spectroscopic constants R e (equilibrium distance) and ω e (harmonic frequency) are also computed. The equilibrium distances are obtained with a relative error smaller than 1%, while the harmonic 1 frequencies are computed with an error of about 10%.

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“…A divisão do trabalho será feita na seguinte seqüência: na próxima seção será dada uma breve introdução ao método Monte Carlo, seguida das considerações sobre o formalismo e aplicação do Monte Carlo em sistemas quânticos. Dentre estas considerações, será feita uma abordagem sobre as duas versões mais utilizadas do Monte Carlo Quântico: o Monte Carlo Quântico Variacional 6,7 e o Monte Carlo Quântico de Difusão [8][9][10][11][12][13] . Discussões sobre a eficiência e limitações do método serão analisadas.…”

Section: Introductionunclassified