skip to main content

SciTech ConnectSciTech Connect

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

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 mE{sub h} after 10{sup 6} Monte Carlo steps.
Authors:
 [1] ;  [2] ;  [1] ;  [3]
  1. Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801 (United States)
  2. (Korea, Republic of)
  3. (Japan)
Publication Date:
OSTI Identifier:
22253597
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Chemical Physics; Journal Volume: 140; Journal Issue: 2; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 97 MATHEMATICAL METHODS AND COMPUTING; ALGORITHMS; DIAGRAMS; EVALUATION; GREEN FUNCTION; INTERACTIONS; MANY-BODY PROBLEM; MONTE CARLO METHOD; PERTURBATION THEORY; POLYNOMIALS; STOCHASTIC PROCESSES