sparse-ir: Optimal compression and sparse sampling of many-body propagators

Markus Wallerberger, Samuel Badr, Shintaro Hoshino, Sebastian Huber, Fumiya Kakizawa, Takashi Koretsune, Yuki Nagai, Kosuke Nogaki, Takuya Nomoto, Hitoshi Mori, Junya Otsuki, Soshun Ozaki, Thomas Plaikner, Rihito Sakurai, Constanze Vogel, Niklas Witt, Kazuyoshi Yoshimi, Hiroshi Shinaoka

Research output: Contribution to journalArticlepeer-review


We introduce sparse-ir, a collection of libraries to efficiently handle imaginary-time propagators, a central object in finite-temperature quantum many-body calculations. We leverage two concepts: firstly, the intermediate representation (IR), an optimal compression of the propagator with robust a priori error estimates, and secondly, sparse sampling, near-optimal grids in imaginary time and imaginary frequency from which the propagator can be reconstructed and on which diagrammatic equations can be solved. IR and sparse sampling are packaged into stand-alone, easy-to-use Python, Julia and Fortran libraries, which can readily be included into existing software. We also include an extensive set of sample codes showcasing the library for typical many-body and ab initio methods.

Original languageEnglish
Article number101266
Publication statusPublished - Feb 2023


  • Fortran
  • Intermediate representation
  • Julia
  • Python
  • Sparse sampling

ASJC Scopus subject areas

  • Software
  • Computer Science Applications


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