### Abstract

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 Greens 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 mE_{h} after 10^{6} Monte Carlo steps.

Original language | English (US) |
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Article number | 024111 |

Journal | Journal of Chemical Physics |

Volume | 140 |

Issue number | 2 |

DOIs | |

State | Published - Jan 14 2014 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*140*(2), [024111]. https://doi.org/10.1063/1.4861561