MatsubaraFunctions.jl: An equilibrium Green's function library in the Julia programming language

TL;DR

MatsubaraFunctions.jl is a Julia library designed to facilitate the computation of equilibrium Green's functions in quantum many-particle systems, emphasizing user-friendliness and computational efficiency.

Contribution

The paper introduces a new Julia library that implements data structures and tools for generalized Green's functions on Matsubara grids, enhancing computational methods in quantum field theory.

Findings

Efficient data structures for Green's functions implemented

Features for extrapolation, interpolation, and symmetry incorporation included

Demonstrations show practical utility and performance strategies

Abstract

The Matsubara Green's function formalism stands as a powerful technique for computing the thermodynamic characteristics of interacting quantum many-particle systems at finite temperatures. In this manuscript, our focus centers on introducing MatsubaraFunctions.jl, a Julia library that implements data structures for generalized n-point Green's functions on Matsubara frequency grids. The package's architecture prioritizes user-friendliness without compromising the development of efficient solvers for quantum field theories in equilibrium. Following a comprehensive introduction of the fundamental types, we delve into a thorough examination of key facets of the interface. This encompasses avenues for accessing Green's functions, techniques for extrapolation and interpolation, as well as the incorporation of symmetries and a variety of parallelization strategies. Examples of increasing complexity serve to demonstrate the practical utility of the library, supplemented by discussions on strategies for sidestepping impediments to optimal performance.