2016/07/14 by Johan Schött, Erik G. C. P. van Loon, Inka L. M. Locht +3
Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Algorithm #Analytic continuation #Applied mathematics #Computer science #Continuation #Iterated function #Mathematical analysis #Mathematics #Noise (video) #Physics #Physics of Superconductivity and Magnetism #Spectral density #Statistical physics #Statistics #Theoretical and Computational Physics #cond-mat.str-el
paper · pdf · doi:10.1103/physrevb.94.245140
published as Phys. Rev. B 94, 245140 (2016) · 13 pages, 9 figures
arxiv created 2016/07/14 · openalex publication_date 2016/12/27 · arxiv updated 2017/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
In this paper we perform a critical assessment of different known methods for the analytical continuation of bosonic functions, namely, the maximum entropy method, the non-negative least-squares method, the non-negative Tikhonov method, the Pad'e approximant method, and a stochastic sampling method. Four functions of different shape are investigated, corresponding to four physically relevant scenarios. They include a simple two-pole model function; two flavors of the tight-binding model on a square lattice, i.e., a single-orbital metallic system and a two-orbital insulating system; and the Hubbard dimer. The effect of numerical noise in the input data on the analytical continuation is discussed in detail. Overall, the stochastic method by A. S. Mishchenko et al. [Phys. Rev. B 62, 6317 (2000)] is shown to be the most reliable tool for input data whose numerical precision is not known. For high-precision input data, this approach is slightly outperformed by the Pad'e approximant method, which combines a good-resolution power with a good numerical stability. Although none of the methods retrieves all features in the spectra in the presence of noise, our analysis provides a useful guideline for obtaining reliable information of the spectral function in cases of practical interest.