Numerical analytic continuation: Answers to well-posed questions

Abstract

We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about properties of the spectral function based solely on the input data. Apart from ensuring consistency with the input data (within their error bars) and the {\it a priori} and {\it a posteriori} (conditional) constraints, it is crucial to reliably characterize the accuracy---or even ambiguity---of the output. We explain how these challenges can be met with two approaches: stochastic optimization with consistent constraints and the modified maximum entropy method. We perform illustrative tests for spectra with a double-peak structure, where we critically examine which spectral properties are accessible and which ones are lost. For an important practical example, we apply our protocol to the Fermi polaron problem.

13 pages, 12 figures

References in corpus (6)

• Observation of Fermi Polarons in a Tunable Fermi Liquid of Ultracold Atoms
• Attractive and repulsive Fermi polarons in two dimensions
• Fermi-Polaron: Diagrammatic Monte Carlo for Divergent Sign-Alternating Series
• Excitation spectra and rf-response near the polaron-to-molecule transition from the functional renormalization group
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• Statistical and computational intelligence approach to analytic continuation in Quantum Monte Carlo
• Extraction of the frequency moments of spectral densities from imaginary-time correlation function data
• Bosonic Nevanlinna Analytic Continuation
• Analytic continuation with Padé decomposition
• Optical signatures of exciton-polarons from diagrammatic Monte Carlo
• Energy response and spatial alignment of the perturbed electron gas
• Energy spectrum of localized quasiparticles renormalized by multi-phonon processes at finite temperature
• Generalized method of Feynman-Pines diagram technique in the theory of energy spectrum of two-level quasiparticle renormalized due to multi-phonon processes at cryogenic temperature