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

Yuichi Motoyama, Kazuyoshi Yoshimi, Junya Otsuki

Research output: Contribution to journalArticlepeer-review

Abstract

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 method that combines the SpM AC with the Padé approximation. This combination, called SpM-Padé, inherits robustness against noise from SpM and low-energy accuracy from Padé, compensating for the disadvantages of each. We demonstrate that the SpM-Padé method yields low-variance and low-biased results with almost the same computational cost as that of the SpM method.

Original languageEnglish
Article number035139
JournalPhysical Review B
Volume105
Issue number3
DOIs
Publication statusPublished - Jan 15 2022

ASJC Scopus subject areas

  • Electronic, Optical and Magnetic Materials
  • Condensed Matter Physics

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