Doran Alexander E, Hirata So
Department of Chemistry, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.
J Chem Phys. 2020 Sep 14;153(10):104112. doi: 10.1063/5.0020583.
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.
在蒙特卡罗多体微扰（MC-MP）方法中，传统的关联校正公式是低维积分乘积的长和式，首先被重铸为电子对和虚时坐标上高维积分的短和式。然后，通过蒙特卡罗方法，根据合适的分布，利用由梅特罗波利斯-黑斯廷斯算法生成的随机坐标来计算这些高维积分。后一种算法虽然在能够对几乎任何分布进行采样方面具有优势，但会在采样坐标中引入自相关，这反过来又增加了积分的统计不确定性，从而增加了计算成本。它还涉及浪费的拒绝移动和初始的“预烧”步骤，并且显示出滞后现象。在此，提出了一种算法，该算法直接生成用于MC-MP方法中相同分布的电子对坐标的随机序列，该序列不存在自相关、拒绝移动、预烧步骤或滞后现象。结果表明，这种直接采样算法分别将二阶和三阶蒙特卡罗多体微扰计算加速了高达222%和38%。
