Analytical solution for time integrals in diagrammatic expansions: Application to real-frequency diagrammatic Monte Carlo

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dc.citation.issue2
dc.citation.rankM21
dc.citation.spage023082
dc.citation.volume3
dc.contributor.authorVučičević, Jakša
dc.contributor.authorStipsić, Pavle
dc.contributor.authorFerrero, Michel
dc.date.accessioned2024-06-14T08:57:40Z
dc.date.available2024-06-14T08:57:40Z
dc.date.issued2021-04-29
dc.description.abstractRecent years have seen a revived interest in the diagrammatic Monte Carlo (DiagMC) methods for interacting fermions on a lattice. A promising recent development allows one to now circumvent the analytical continuation of dynamic observables in DiagMC calculations within the Matsubara formalism. This is made possible by symbolic algebra algorithms, which can be used to analytically solve the internal Matsubara frequency summations of Feynman diagrams. In this paper, we take a different approach and show that it yields improved results. We present a closed-form analytical solution of imaginary-time integrals that appear in the time-domain formulation of Feynman diagrams. We implement and test a DiagMC algorithm based on this analytical solution and show that it has numerous significant advantages. Most importantly, the algorithm is general enough for any kind of single-time correlation function series, involving any single-particle vertex insertions. Therefore, it readily allows for the use of action-shifted schemes, aimed at improving the convergence properties of the series. By performing a frequency-resolved action-shift tuning, we are able to further improve the method and converge the self-energy in a nontrivial regime, with only 3-4 perturbation orders. Finally, we identify time integrals of the same general form in many commonly used Monte Carlo algorithms and therefore expect a broader usage of our analytical solution.
dc.identifier.doi10.1103/physrevresearch.3.023082
dc.identifier.issn2643-1564
dc.identifier.scopus2-s2.0-85107643068
dc.identifier.urihttps://pub.ipb.ac.rs/handle/123456789/95
dc.identifier.wos000648508300003
dc.language.isoen
dc.publisherAmerican Physical Society (APS)
dc.relation.ispartofPhysical Review Research
dc.relation.ispartofabbrPhys. rev. res.
dc.rightsopenAccess
dc.titleAnalytical solution for time integrals in diagrammatic expansions: Application to real-frequency diagrammatic Monte Carlo
dc.typeArticle
dc.type.versionpublishedVersion
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