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@ARTICLE{Ghanem:877867,
      author       = {Ghanem, Khaldoon and Koch, Erik},
      title        = {{E}xtending the average spectrum method: {G}rid point
                      sampling and density averaging},
      journal      = {Physical review / B},
      volume       = {102},
      number       = {3},
      issn         = {0163-1829},
      address      = {Woodbury, NY},
      publisher    = {Inst.},
      reportid     = {FZJ-2020-02485},
      pages        = {035114},
      year         = {2020},
      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.},
      cin          = {JSC},
      ddc          = {530},
      cid          = {I:(DE-Juel1)JSC-20090406},
      pnm          = {511 - Computational Science and Mathematical Methods
                      (POF3-511)},
      pid          = {G:(DE-HGF)POF3-511},
      typ          = {PUB:(DE-HGF)16},
      UT           = {WOS:000545539900007},
      doi          = {10.1103/PhysRevB.102.035114},
      url          = {https://juser.fz-juelich.de/record/877867},
}