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Robust analytic continuation combining the advantages of the sparse modeling approach and Pade approximation

y-motoyama / Robust analytic continuation combining the advantages of the sparse modeling approach and Pade approximation

電子状態計算（固体物理）強相関電子系・有効模型機械学習CC BY 4.0
更新: 2022-06-29

概要

Analytic continuation (AC) from the imaginary-time Green’s function to the spectral function is a crucial process for numerical studies of the dynamical properties of quantum many-body systems. This process, however, is an ill-posed problem; that is, the obtained spectrum is unstable against the noise of the Green’s function. Though several numerical methods have been developed, each of them has its own advantages and disadvantages. The sparse modeling (SpM) AC method, for example, is robust against the noise of the Green’s function but suffers from unphysical oscillations in the low energy region. We propose a new method that combines the SpM AC with the Pade approximation. This combination, called SpM-Pade, inherits robustness against noise from SpM and low-energy accuracy from Pade, compensating for the disadvantages of each. We demonstrate that the SpMPad´e method yields low-variance and low-biased results with almost the same computational cost as that of the SpM method.

URL
https://isspns-gitlab.issp.u-tokyo.ac.jp/y-motoyama/robust-analytic-continuation-combining-the-advantages-of-the-sparse-modeling-approach-and-pade-approximation
DOI
10.1103/PhysRevB.105.035139
被引用数
15 件（OpenAlex、2026-10-05 時点）
著者
Yuichi Motoyama, Kazuyoshi Yoshimi, Junya Otsuki
ライセンス
CC BY 4.0
キーワード
analytic continuationsparse modelsPadé approximantsimaginary-time Green's functionsspectral functionill-posed inverse problemsnoise robustnessunphysical oscillations（論文のキーワード、OpenAlex より）
カテゴリ
電子状態計算（固体物理）, 強相関電子系・有効模型, 機械学習
関連文献
Yuichi Motoyama, Kazuyoshi Yoshimi, and Junya Otsuki, "Robust analytic continuation combining the advantages of the sparse modeling approach and the Padé approximation", Phys. Rev. B 105, 035139 (2022).
関連ソフトウェア
SpM, DCore (リンク先: PASUMS ソフトウェアカタログ)
連絡先
y-motoyama__at__issp.u-tokyo.ac.jp (__at__ を @ に置き換えてください。)

論文と引用

このデータを利用した場合は、次の論文を引用してください。

Yuichi Motoyama, Kazuyoshi Yoshimi, and Junya Otsuki, "Robust analytic continuation combining the advantages of the sparse modeling approach and the Padé approximation", Physical review. B./Physical review. B 105(3) (2022). https://doi.org/10.1103/PhysRevB.105.035139

論文を読む（オープンアクセス） ↗
BibTeX を表示
@article{Motoyama_2022, title={Robust analytic continuation combining the advantages of the sparse modeling approach and the Padé approximation}, volume={105}, ISSN={2469-9969}, url={http://dx.doi.org/10.1103/physrevb.105.035139}, DOI={10.1103/physrevb.105.035139}, number={3}, journal={Physical Review B}, publisher={American Physical Society (APS)}, author={Motoyama, Yuichi and Yoshimi, Kazuyoshi and Otsuki, Junya}, year={2022}, month=Jan }

書誌情報とオープンアクセスのリンクは OpenAlex、BibTeX は doi.org（出版社が登録した情報）から取得しています。

リンク

💻 リポジトリを開く📦 ZIP でダウンロード

README

Robust analytic continuation combining the advantages of the sparse modeling approach and Pade approximation

Reference

License of data

  • CC BY 4.0

Directory Structure

  • README.md
  • LICENSE
  • data
    • three_peaks
      • Data for three-peak spectrum
        • Fig. 1
      • Gtau.in.dos
        • "Exact" spectrum
      • noise_1e-3
        • Large noise data (Gaussian noise with σ=1e-3)
        • id_*
          • Samples
          • Gtau.in
            • Green's function G(τ) (input)
          • METHOD/spectrum.dat
            • Spectrum ρ(ω) reconstructed by METHOD (output)
        • param.in
          • Input file of SpM.out
        • mean_METHOD.dat
          • Mean and stddev of 30 spectra
      • noise_1e-5
        • Small noise data (Gaussian noise with σ=1e-5)
      • three_peaks.toml
        • Input file of gen_Gtau_peaks.py
      • stat.py
        • Calculator of mean and stddev of 30 spectra
      • plt_*.plt
        • Gnuplot files
    • two_peaks
      • Data for three-peak spectrum
        • Fig. 2, 3, 5
      • Gtau.in.dos
        • "Exact" spectrum
      • noise_1e-4
        • Large noise data (Gaussian noise with σ=1e-4)
        • id_*
          • Samples
          • Gtau.in
            • Green's function G(τ) (input)
          • METHOD/spectrum.dat
            • Spectrum ρ(ω) reconstructed by METHOD (output)
        • param.in
          • Input file of SpM.out
        • mean_METHOD.dat
          • Mean and stddev of 30 spectra
      • noise_1e-5
        • Medium noise data (Gaussian noise with σ=1e-5)
      • noise_1e-6
        • Small noise data (Gaussian noise with σ=1e-6)
      • two_peaks.toml
        • Input file of gen_Gtau_peaks.py
      • stat.py
        • Calculator of mean and stddev of 30 spectra
      • plt_*.plt
        • Gnuplot files
    • dmft
      • Data for DMFT
        • Fig. 6
      • dmft_square_ctseg.ini
        • Input file of DCore
      • param.in
        • Input file of SpM
      • read.py
        • Calculator of G(τ) from sim.h5 (output of ALPS/CTHYB)
      • Gt_0.dat
        • G(τ)
      • plt.plt
        • Gnuplot file
      • work/imp_shell0_ite40
        • I/O of ALPS/CTHYB (last iteration)

出典: https://isspns-gitlab.issp.u-tokyo.ac.jp/y-motoyama/robust-analytic-continuation-combining-the-advantages-of-the-sparse-modeling-approach-and-pade-approximation の README

更新状況

更新最終更新: 2022-06-29 ()