Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA.
J Chem Phys. 2014 Jan 14;140(2):024111. doi: 10.1063/1.4861561.
A new, alternative set of interpretation rules of Feynman-Goldstone diagrams for many-body perturbation theory is proposed, which translates diagrams into algebraic expressions suitable for direct Monte Carlo integrations. A vertex of a diagram is associated with a Coulomb interaction (rather than a two-electron integral) and an edge with the trace of a Green's function in real space and imaginary time. With these, 12 diagrams of third-order many-body perturbation (MP3) theory are converted into 20-dimensional integrals, which are then evaluated by a Monte Carlo method. It uses redundant walkers for convergence acceleration and a weight function for importance sampling in conjunction with the Metropolis algorithm. The resulting Monte Carlo MP3 method has low-rank polynomial size dependence of the operation cost, a negligible memory cost, and a naturally parallel computational kernel, while reproducing the correct correlation energies of small molecules within a few mEh after 10(6) Monte Carlo steps.
提出了一种新的、替代的费曼-戈德斯通图的多体微扰论解释规则，它将图转化为适合直接蒙特卡罗积分的代数表达式。图的一个顶点与库仑相互作用（而不是两个电子积分）相关联，而一个边与实空间和虚时间中的格林函数的迹相关联。利用这些规则，将三阶多体微扰（MP3）理论的 12 个图转化为 20 维积分，然后通过蒙特卡罗方法进行评估。它使用冗余步行者进行收敛加速，并结合 metropolis 算法使用权函数进行重要性采样。由此产生的蒙特卡罗 MP3 方法具有低阶多项式的运算成本依赖性，几乎可以忽略不计的内存成本，以及自然并行的计算内核，而在经过 10^6 次蒙特卡罗步骤后，它可以在几个毫电子伏特内再现小分子的正确相关能量。
