In the Monte Carlo many-body perturbation (MC-MP) method, the conventional correlation-correction formula, which is a long sum of products of low-dimensional integrals, is first recast into a short sum of high-dimensional integrals over electron-pair and imaginary-time coordinates. These high-dimensional integrals are then evaluated by the Monte Carlo method with random coordinates generated by the Metropolis–Hasting algorithm according to a suitable distribution. The latter algorithm, while advantageous in its ability to sample nearly any distribution, introduces autocorrelation in sampled coordinates, which, in turn, increases the statistical uncertainty of the integrals and thus the computational cost. It also involves wasteful rejected moves and an initial “burn-in” step as well as displays hysteresis. Here, an algorithm is proposed that directly produces a random sequence of electron-pair coordinates for the same distribution used in the MC-MP method, which is free from autocorrelation, rejected moves, a burn-in step, or hysteresis. This direct-sampling algorithm is shown to accelerate second- and third-order Monte Carlo many-body perturbation calculations by up to 222% and 38%, respectively.
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Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling
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14 September 2020
Research Article|
September 10 2020
Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling
Special Collection:
Frontiers of Stochastic Electronic Structure Calculations
Alexander E. Doran
;
Alexander E. Doran
a)
Department of Chemistry, University of Illinois at Urbana-Champaign
, Urbana, Illinois 61801, USA
a)Author to whom correspondence should be addressed: [email protected]
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Alexander E. Doran
a)
So Hirata
b)
Department of Chemistry, University of Illinois at Urbana-Champaign
, Urbana, Illinois 61801, USA
a)Author to whom correspondence should be addressed: [email protected]
b)
Electronic mail: [email protected]
Note: This paper is part of the JCP Special Topic on Frontiers of Stochastic Electronic Structure Calculations.
J. Chem. Phys. 153, 104112 (2020)
Article history
Received:
July 01 2020
Accepted:
August 17 2020
Citation
Alexander E. Doran, So Hirata; Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling. J. Chem. Phys. 14 September 2020; 153 (10): 104112. https://doi.org/10.1063/5.0020583
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