Journal Article

FZJ-2020-02485

http://join2-wiki.gsi.de/foswiki/pub/Main/Artwork/join2_logo100x88.png Extending the average spectrum method: Grid point sampling and density averaging

Ghanem, K.FZJ* ; Koch, E. (Corresponding author)FZJ*

2020
Inst. Woodbury, NY

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Please use a persistent id in citations: http://hdl.handle.net/2128/25245  doi:10.1103/PhysRevB.102.035114

Abstract: Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating over all nonnegative spectra weighted by how well they fit the data. In a recent paper, we found that discretizing the functional integral, as in Feynman's path-integrals, does not have a well-defined continuum limit. Instead, the limit depends on the discretization grid whose choice may strongly bias the results. In this paper, we demonstrate that sampling the grid points, instead of keeping them fixed, also changes the functional integral limit and rather helps to overcome the bias considerably. We provide an efficient algorithm for doing the sampling and show how the density of the grid points acts now as a default model with a significantly reduced biasing effect. The remaining bias depends mainly on the width of the grid density, so we go one step further and average also over densities of different widths. For a certain class of densities, including Gaussian and exponential ones, this width averaging can be done analytically, eliminating the need to specify this parameter without introducing any computational overhead.

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Contributing Institute(s):

1. Jülich Supercomputing Center (JSC)

Research Program(s):

1. 511 - Computational Science and Mathematical Methods (POF3-511) (POF3-511)

Appears in the scientific report 2020

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Database coverage:
; ; ; Clarivate Analytics Master Journal List ; Current Contents - Electronics and Telecommunications Collection ; Current Contents - Physical, Chemical and Earth Sciences ; Ebsco Academic Search ; Essential Science Indicators ; IF < 5 ; JCR ; SCOPUS ; Science Citation Index ; Science Citation Index Expanded ; Web of Science Core Collection

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