Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams.
Identifieur interne : 001156 ( Main/Corpus ); précédent : 001155; suivant : 001157Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams.
Auteurs : Soohaeng Yoo Willow ; So HirataSource :
- The Journal of chemical physics [ 1089-7690 ] ; 2014.
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 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.
DOI: 10.1063/1.4861561
PubMed: 24437869
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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. </div></front></TEI><pubmed><MedlineCitation Status="PubMed-not-MEDLINE" Owner="NLM"><PMID Version="1">24437869</PMID><DateCompleted><Year>2014</Year><Month>09</Month><Day>15</Day></DateCompleted><DateRevised><Year>2014</Year><Month>01</Month><Day>20</Day></DateRevised><Article PubModel="Print"><Journal><ISSN IssnType="Electronic">1089-7690</ISSN><JournalIssue CitedMedium="Internet"><Volume>140</Volume><Issue>2</Issue><PubDate><Year>2014</Year><Month>Jan</Month><Day>14</Day></PubDate></JournalIssue><Title>The Journal of chemical physics</Title><ISOAbbreviation>J Chem Phys</ISOAbbreviation></Journal><ArticleTitle>Stochastic, real-space, imaginary-time evaluation of third-order Feynman-Goldstone diagrams.</ArticleTitle><Pagination><MedlinePgn>024111</MedlinePgn></Pagination><ELocationID EIdType="doi" ValidYN="Y">10.1063/1.4861561</ELocationID><Abstract><AbstractText>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. </AbstractText></Abstract><AuthorList CompleteYN="Y"><Author ValidYN="Y"><LastName>Willow</LastName><ForeName>Soohaeng Yoo</ForeName><Initials>SY</Initials><AffiliationInfo><Affiliation>Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA.</Affiliation></AffiliationInfo></Author><Author ValidYN="Y"><LastName>Hirata</LastName><ForeName>So</ForeName><Initials>S</Initials><AffiliationInfo><Affiliation>Department of Chemistry, University of Illinois at Urbana-Champaign, 600 South Mathews Avenue, Urbana, Illinois 61801, USA.</Affiliation></AffiliationInfo></Author></AuthorList><Language>eng</Language><PublicationTypeList><PublicationType UI="D016428">Journal Article</PublicationType></PublicationTypeList></Article><MedlineJournalInfo><Country>United States</Country><MedlineTA>J Chem Phys</MedlineTA><NlmUniqueID>0375360</NlmUniqueID><ISSNLinking>0021-9606</ISSNLinking></MedlineJournalInfo></MedlineCitation><PubmedData><History><PubMedPubDate PubStatus="entrez"><Year>2014</Year><Month>1</Month><Day>21</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="pubmed"><Year>2014</Year><Month>1</Month><Day>21</Day><Hour>6</Hour><Minute>0</Minute></PubMedPubDate><PubMedPubDate PubStatus="medline"><Year>2014</Year><Month>1</Month><Day>21</Day><Hour>6</Hour><Minute>1</Minute></PubMedPubDate></History><PublicationStatus>ppublish</PublicationStatus><ArticleIdList><ArticleId IdType="pubmed">24437869</ArticleId><ArticleId IdType="doi">10.1063/1.4861561</ArticleId></ArticleIdList></PubmedData></pubmed></record>Pour manipuler ce document sous Unix (Dilib)
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