Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams

Soohaeng Yoo Willow, So Hirata

Research output: Contribution to journalArticlepeer-review


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 mEh after 106 Monte Carlo steps.

Original languageEnglish (US)
Article number024111
JournalJournal of Chemical Physics
Issue number2
StatePublished - Jan 14 2014

ASJC Scopus subject areas

  • General Physics and Astronomy
  • Physical and Theoretical Chemistry


Dive into the research topics of 'Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams'. Together they form a unique fingerprint.

Cite this