LIBAMI: Implementation of algorithmic Matsubara integration

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 summary Program Title: libamiCPC 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. References [1] Amir Taheridehkordi, S.H. Curnoe, J.P.F. LeBlanc, Algorithmic Matsubara integration for Hubbard-like models, Phys. Rev. B 99 (2019) 035120. (C) 2022 Elsevier B.V. All rights reserved.

Automated summary

libami is a lightweight implementation of algorithmic Matsubara integration (AMI) written in C++. It can analytically resolve the sequence of nested Matsubara integrals that arise in Feynman perturbative expansions in condensed matter systems. It provides a method to generate and store the analytic solution to temporal Matsubara sums, which is valid in any dimensionality, dispersion, and temperature.