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

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

Research output: Contribution to journalArticle

1 Citation (Scopus)

Abstract

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
Volume244
DOIs
Publication statusPublished - Nov 2019

Fingerprint

time functions
Inverse problems
Green's function
Green's functions
Error statistics
Computer programming languages
licensing
programming languages
files
statistics
excitation
Monte Carlo simulation
simulation

Keywords

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

ASJC Scopus subject areas

  • Hardware and Architecture
  • Physics and Astronomy(all)

Cite this

SpM : Sparse modeling tool for analytic continuation of imaginary-time Green's function. / Yoshimi, Kazuyoshi; Otsuki, Junya; Motoyama, Yuichi; Ohzeki, Masayuki; Shinaoka, Hiroshi.

In: Computer Physics Communications, Vol. 244, 11.2019, p. 319-323.

Research output: Contribution to journalArticle

Yoshimi, Kazuyoshi ; Otsuki, Junya ; Motoyama, Yuichi ; Ohzeki, Masayuki ; Shinaoka, Hiroshi. / SpM : Sparse modeling tool for analytic continuation of imaginary-time Green's function. In: Computer Physics Communications. 2019 ; Vol. 244. pp. 319-323.
@article{7c8af944bdcb4491bce9b21cd283591b,
title = "SpM: Sparse modeling tool for analytic continuation of imaginary-time Green's function",
abstract = "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.",
keywords = "Analytic continuation, Imaginary-time/Matsubara Green's function, Sparse modeling",
author = "Kazuyoshi Yoshimi and Junya Otsuki and Yuichi Motoyama and Masayuki Ohzeki and Hiroshi Shinaoka",
year = "2019",
month = "11",
doi = "10.1016/j.cpc.2019.07.001",
language = "English",
volume = "244",
pages = "319--323",
journal = "Computer Physics Communications",
issn = "0010-4655",
publisher = "Elsevier",

}

TY - JOUR

T1 - SpM

T2 - Sparse modeling tool for analytic continuation of imaginary-time Green's function

AU - Yoshimi, Kazuyoshi

AU - Otsuki, Junya

AU - Motoyama, Yuichi

AU - Ohzeki, Masayuki

AU - Shinaoka, Hiroshi

PY - 2019/11

Y1 - 2019/11

N2 - 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.

AB - 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.

KW - Analytic continuation

KW - Imaginary-time/Matsubara Green's function

KW - Sparse modeling

UR - http://www.scopus.com/inward/record.url?scp=85069706257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85069706257&partnerID=8YFLogxK

U2 - 10.1016/j.cpc.2019.07.001

DO - 10.1016/j.cpc.2019.07.001

M3 - Article

AN - SCOPUS:85069706257

VL - 244

SP - 319

EP - 323

JO - Computer Physics Communications

JF - Computer Physics Communications

SN - 0010-4655

ER -