Welcome to SpM’s documentation!

This is a documentation of Sparse Modeling (SpM) tool for analytical continuation.

What is SpM ?

A sparse-modeling tool for computing the spectral function from the imaginary-time Green function. It removes statistical errors in quantum Monte Carlo data, and performs a stable analytical continuation. The obtained spectral function fulfills the non-negativity and the sum rule. The computation is fast and free from tuning parameters.


This package is distributed under GNU General Public License version 3 (GPL v3).

When you publish a publication that includes results obtained using this package, we kindly ask you to cite the following articles

  • SpM method

    J. Otsuki, M. Ohzeki, H. Shinaoka, K. Yoshimi, “Sparse modeling approach to analytical continuation of imaginary-time quantum Monte Carlo dataPhys. Rev. E 95, 061302(R) (2017).

  • SpM package

    K. Yoshimi, J. Otsuki, Y. Motoyama, M. Ohzeki, and H. Shinaoka, “SpM: Sparse modeling tool for analytic continuation of imaginary-time Green’s functionComput. Phys. Commun. 244, 319-323 (2019).

  • SpM-Pade method (if you use)

    Y. Motoyama, K. Yoshimi, and J. Otsuki, “Robust analytic continuation combining the advantages of the sparse modeling approach and Pade approximation”, [arXiv:2109.08370](https://arxiv.org/abs/2109.08370).