The sparse-ir ecosystem

sparse-ir is a family of libraries for compact representations of imaginary-time Green’s functions: the intermediate representation (IR), the discrete Lehmann representation (DLR), sparse sampling, and minimal pole representations (MiniPole). This site is the entry point for all of them: the theory, the history, the notation they share, and where to find each library’s documentation.

The libraries are maintained by SpM-lab, which also develops tools for analytic continuation.

Where to go

If you want to …	Go to
know what IR, DLR and MiniPole are, where they came from, and which to use	IR, DLR and MiniPole: history and comparison
check a symbol or a sign convention, or find the matching name in a library	Notation and conventions
learn the basics step by step	Basic theory: Green’s functions, IR, sparse sampling, DLR
pick a library and find its installation guide, API reference and examples	Libraries
run worked examples (GW, DMFT, FLEX, TPSC, Eliashberg, analytic continuation)	Python and Julia tutorial, Rust guide

The libraries at a glance

Language	Library	Documentation
Python	sparse-ir (pip install sparse-ir)	sparse-ir.readthedocs.io
Julia	SparseIR.jl (] add SparseIR)	SparseIR.jl documentation
Rust, C, Fortran	sparse-ir-rs (crates sparse-ir, sparse-ir-capi)	Rust guide

sparse-ir-rs is the shared backend: the Python and Julia libraries call its C API (libsparseir), and it ships the Fortran bindings. New features land there first.

Citing

If you use these libraries, please cite M. Wallerberger et al., sparse-ir: Optimal compression and sparse sampling of many-body propagators, SoftwareX 21, 101266 (2023), and the papers on the methods you use, listed in history and comparison.