LIBAMI: Implementation of algorithmic Matsubara integration

• Published in: Computer physics communications Vol. 280; p. 108469
• Main Authors: Elazab, Hossam, McNiven, B.D.E., LeBlanc, J.P.F.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2022
• Subjects: Algorithmic Matsubara integration; Diagrammatic Monte Carlo; Feynman diagrams; Feynman diagrams; Diagrammatic Monte Carlo; Algorithmic Matsubara integration
• ISSN: 0010-4655; 1879-2944
• DOI: 10.1016/j.cpc.2022.108469

We present libami, a lightweight implementation of algorithmic Matsubara integration (AMI) written in C++. AMI is a tool for analytically resolving the sequence of nested Matsubara integrals that arise in virtually all Feynman perturbative expansions. Program Title: libami CPC Library link to program files:https://doi.org/10.17632/zkwwmbnm6m.1 Developer's repository link:https://github.com/jpfleblanc/libami Licensing provisions: GPLv3 Programming language:C++ Nature of problem: Perturbative expansions in condensed matter systems are formulated on the imaginary frequency/time axis and are often represented as a series of Feynman diagrams, which involve a sequence of nested integrals/summations over internal Matsubara indices as well as other internal variables. Solution method:libami provides a minimal framework to symbolically generate and store the analytic solution to the temporal Matsubara sums through repeated application of multipole residue theorems. The solution can be applied to any frequency-independent interaction expansion. Once generated, the analytic solution is valid in any dimensionality with any dispersion at arbitrary temperature. Additional comments including restrictions and unusual features: Requires C++11 standard. Optional compilation with boost-multiprecision library. [1]Amir Taheridehkordi, S.H. Curnoe, J.P.F. LeBlanc, Algorithmic Matsubara integration for Hubbard-like models, Phys. Rev. B 99 (2019) 035120.