TY - JOUR

T1 - Convergence acceleration of Monte Carlo many-body perturbation methods by direct sampling

AU - Doran, Alexander E

AU - Hirata, So

N1 - Funding Information:
This work was supported by the Center for Scalable, Predictive methods for Excitation and Correlated phenomena (SPEC), which is funded by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences, Chemical Sciences, Geosciences, and Biosciences Division, as a part of the Computational Chemical Sciences Program and also by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Grant No. DE-SC0006028. It is also part of the Blue Waters sustained-petascale computing project, which is supported by the National Science Foundation (Award Nos. OCI-0725070 and ACI-1238993) and the state of Illinois. Blue Waters is a joint effort of the University of Illinois at Urbana-Champaign and its National Center for Supercomputing Applications.

PY - 2020/9/14

Y1 - 2020/9/14

N2 - 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.

AB - 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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U2 - 10.1063/5.0020583

DO - 10.1063/5.0020583

M3 - Article

C2 - 32933294

VL - 153

SP - 104112

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 10

M1 - 104112

ER -