DOI: 10.1063/1.463411. A Bayesian analysis of Green’s function Monte Carlo correlation functions

A Bayesian analysis of Green’s function Monte Carlo correlation functions

10.1063/1.463411

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

Imaginary-time correlation functions calculated by quantum Monte Carlo (QMC) are analyzed using the maximum entropy method (MaxEnt) to determine the ground-state energy and spectral overlap function. In contrast to earlier applications of MaxEnt, the data is obtained from importanced-sampled zero-temperature quantum Monte Carlo simulations. The analysis includes two steps. First, that spectral overlap function and ground state energy which maximizes the entropy and agrees with the QMC correlation functions is obtained. Then the errors in the energy are evaluated by averaging over all the possible images (average MaxEnt method), the multidimensional integrals being computed using the Metropolis algorithm. The central feature of this approach is that all the information present in the correlation functions is used in the only way consistent with fundamental probabilistic hypotheses. This allows us to fully exploit the information contained in the correlation functions at small imaginary times, thus avoiding large statistical fluctuations associated with large imaginary times. In addition, the computed errors include both the statistical errors and systematic extrapolation errors. The method is illustrated with a harmonic oscillator and the four-electron LiH molecule.

Bibliography

Caffarel, M., & Ceperley, D. M. (1992). A Bayesian analysis of Greenâs function Monte Carlo correlation functions. The Journal of Chemical Physics, 97(11), 8415â8423.

Authors 2

M. Caffarel (first)
D. M. Ceperley (additional)

References 21 Referenced 41

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{'key': '2024020618042829200_r2', 'first-page': '646', 'volume': '131', 'year': '1984', 'journal-title': 'IEEE Proc.'} / IEEE Proc. (1984)
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{'key': '2024020618042829200_r4'}
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Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:22 a.m.)
Deposited	1 year, 6 months ago (Feb. 6, 2024, 5:49 p.m.)
Indexed	1 year, 6 months ago (Feb. 11, 2024, 6:42 a.m.)
Issued	32 years, 8 months ago (Dec. 1, 1992)
Published	32 years, 8 months ago (Dec. 1, 1992)
Published Print	32 years, 8 months ago (Dec. 1, 1992)

Funders 0

None

BibTeX

@article{Caffarel_1992, title={A Bayesian analysis of Green’s function Monte Carlo correlation functions}, volume={97}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.463411}, DOI={10.1063/1.463411}, number={11}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Caffarel, M. and Ceperley, D. M.}, year={1992}, month=dec, pages={8415–8423} }

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