LIBAMI: Implementation of algorithmic Matsubara integration

Abstract

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 summaryProgram Title: libamiCPC Library link to program files:https://doi.org/10.17632/zkwwmbnm6m.1Developer's repository link:https://github.com/jpfleblanc/libamiLicensing provisions: GPLv3Programming 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.