SpM: Sparse modeling tool for analytic continuation of imaginary-time Green's function

Kazuyoshi Yoshimi, Junya Otsuki, Yuichi Motoyama, Masayuki Ohzeki, Hiroshi Shinaoka

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1 Citation (Scopus)


We present SpM, a sparse modeling tool for the analytic continuation of imaginary-time Green's function, licensed under GNU General Public License version 3. In quantum Monte Carlo simulation, dynamic physical quantities such as single-particle and magnetic excitation spectra can be obtained by applying analytic continuation to imaginary-time data. However, analytic continuation is an ill-conditioned inverse problem and thus sensitive to noise and statistical errors. SpM provides stable analytic continuation against noise by means of a modern regularization technique, which automatically selects bases that contain relevant information unaffected by noise. This paper details the use of this program and shows some applications. Program summary: Program Title: SpM Program Files doi: http://dx.doi.org/10.17632/ycmpsnv5yx.1 Licensing provisions: GNU General Public License version 3 Programming language: C++. External routines/libraries: BLAS, LAPACK, and CPPLapack libraries. Nature of problem: The analytic continuation of imaginary-time input data to real-frequency spectra is known to be an ill-conditioned inverse problem and very sensitive to noise and the statistic errors. Solution method: By using a modern regularization technique, analytic continuation is made robust against noise since the basis that is unaffected by the noise is automatically selected.

Original languageEnglish
Pages (from-to)319-323
Number of pages5
JournalComputer Physics Communications
Publication statusPublished - Nov 2019



  • Analytic continuation
  • Imaginary-time/Matsubara Green's function
  • Sparse modeling

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)

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