Automated evaluation of imaginary time strong coupling diagrams by sum-of-exponentials hybridization fitting

Huang, Zhen (author), Golež, Denis (author), Strand, Hugo U. R. (author), Kaye, Jason (author)

We present an efficient separation of variables algorithm for the evaluation of imaginary time Feynman diagrams appearing in the bold pseudo-particle strong coupling expansion of the Anderson impurity model. The algorithm uses a fitting method based on AAA rational approximation and numerical optimization to obtain a sum-of-exponentials expansion of the hybridization function, which is then used to decompose the diagrams. A diagrammatic formulation of the algorithm leads to an automated procedure for diagrams of arbitrary order and topology. We also present methods of stabilizing the self-consistent solution of the pseudo-particle Dyson equation. The result is a low-cost and high-order accurate impurity solver for quantum embedding methods using general multi-orbital hybridization functions at low temperatures, appropriate for low-to-intermediate expansion orders. In addition to other benchmark examples, we use our solver to perform a dynamical mean-field theory study of a minimal model of the strongly correlated compound Ca$_2$RuO$_4$, describing the anti-ferromagnetic transition and the in- and out-of-plane anisotropy induced by spin-orbit coupling.

• Language: English
• Keywords: condensed matter physics, quantum physics, many-body systems, Hubbard model, Anderson model
• Work type: Article
• Typology: 1.01 - Original Scientific Article
• Organization: FMF - Faculty of Mathematics and Physics
• Publication status: Published
• Publication version: Version of Record
• Year: 2025
• Number of pages: 39 str.
• Numbering: Vol. 19, iss. 5
• PID: 20.500.12556/RUL-177292
• UDC: 538.9
• ISSN on article: 2542-4653
• DOI: 10.21468/SciPostPhys.19.5.121
• COBISS.SI-ID: 262306819
• Publication date in RUL: 19.12.2025

Record is a part of a journal

• Title: SciPost physics
• Publisher: SciPost Foundation
• ISSN: 2542-4653
• COBISS.SI-ID: 526154521

Licences

• License: CC BY 4.0, Creative Commons Attribution 4.0 International
• Link: http://creativecommons.org/licenses/by/4.0/
• Description: This is the standard Creative Commons license that gives others maximum freedom to do what they want with the work as long as they credit the author.

Secondary language

• Language: Slovenian
• Keywords: fizika kondenzirane snovi, kvantna fizika, večdelčni sistemi, Hubbardov model, Andersonov model