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
Overview
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
- Citations
- 15 (OpenAlex, as of 2026-10-05)
- Authors
- Yuichi Motoyama, Kazuyoshi Yoshimi, Junya Otsuki
- License
- CC BY 4.0
- Keywords
- analytic continuationsparse modelsPadé approximantsimaginary-time Green's functionsspectral functionill-posed inverse problemsnoise robustnessunphysical oscillations (keywords of the paper, from OpenAlex)
- Category
- Electronic structure (solid state physics), Strong correlation/effective models, Machine learning
- References
- 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).
- Related software
- SpM, DCore (Links to: PASUMS software catalog)
- Contact
- y-motoyama__at__issp.u-tokyo.ac.jp (Please replace __at__ with @.)
Paper and citation
If you use this data, please cite the following paper.
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
Show BibTeX
@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 }Bibliographic details and the open-access link are from OpenAlex; the BibTeX is from doi.org (as registered by the publisher).
README
Robust analytic continuation combining the advantages of the sparse modeling approach and Pade approximation
Reference
- Yuichi Motoyama, Kazuyoshi Yoshimi, and Junya Otsuki, Phys. Rev. B 105, 035139 (2022)
License of data
- CC BY 4.0
Directory Structure
README.mdLICENSEdatathree_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)
- Spectrum ρ(ω) reconstructed by
param.in- Input file of
SpM.out
- Input file of
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
- Input file of
stat.py- Calculator of mean and stddev of 30 spectra
plt_*.plt- Gnuplot files
- Data for three-peak spectrum
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)
- Spectrum ρ(ω) reconstructed by
param.in- Input file of
SpM.out
- Input file of
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
- Input file of
stat.py- Calculator of mean and stddev of 30 spectra
plt_*.plt- Gnuplot files
- Data for three-peak spectrum
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)
- Calculator of G(τ) from
Gt_0.dat- G(τ)
plt.plt- Gnuplot file
work/imp_shell0_ite40- I/O of ALPS/CTHYB (last iteration)
- Data for DMFT