A comparison between methods of analytical continuation for bosonic functions
arXiv:1607.04212 · doi:10.1103/PhysRevB.94.245140
Abstract
In this article 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-square method, the non-negative Tikhonov method, the Padé approximant method, and a stochastic sampling method. Three functions of different shape are investigated, corresponding to three physically relevant scenarios. They include a simple two-pole model function and two flavours of the non-interacting Hubbard model on a square lattice, i.e. a single-orbital metallic system and a two-orbitals insulating system. The effect of numerical noise in the input data on the analytical continuation is discussed in detail. Overall, the stochastic method by Mishchenko et al. [Phys. Rev. B \textbf{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 Padé 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.
13 pages, 9 figures
References in corpus (10)
- Continuous-time Monte Carlo methods for quantum impurity models
- Screening and Non-local Correlations in the Extended Hubbard Model from Self-Consistent Combined GW and Dynamical Mean Field Theory
- Beyond extended dynamical mean-field theory: Dual boson approach to the two-dimensional extended Hubbard model
- Spectral Properties of Correlated Materials: Local Vertex and Non-Local Two-Particle Correlations from Combined GW and Dynamical Mean Field Theory
- Extended dynamical mean-field study of the Hubbard model with long range interactions
- Distribution of Localized States from Fine Analysis of Electron Spin Resonance Spectra in Organic Transistors
- Plasmons in strongly correlated systems: spectral weight transfer and renormalized dispersion
- Collective Charge Excitations of Strongly Correlated Electrons, Vertex Corrections and Gauge Invariance
- Analytical continuation of imaginary axis data using maximum entropy
- Distribution of localized states from fine analysis of electron spin resonance spectra of organic semiconductors: Physical meaning and methodology