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

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