Numerical analytic continuation: Answers to well-posed questions

Olga Goulko, Andrey S. Mishchenko, Lode Pollet, Nikolay Prokof'Ev, Boris Svistunov

Research output: Contribution to journalArticlepeer-review


We formulate the problem of numerical analytic continuation in a way that lets us draw meaningful conclusions about the 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 a priori and 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 (second peak position and its spectral weight) and which ones are lost (second peak width/shape). For an important practical example, we apply our protocol to the Fermi polaron problem.

Original languageEnglish
Article number014102
JournalPhysical Review B
Issue number1
StatePublished - 6 Jan 2017
Externally publishedYes


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