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  • Letter
  • Open Access

Functional interpolation expansion for nonequilibrium correlated impurities

Daniel Werner* and Enrico Arrigoni†

  • *Contact author: daniel.werner96@posteo.at
  • †Contact author: arrigoni@tugraz.at
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Phys. Rev. Research 7, L022044 – Published 29 May, 2025

DOI: https://doi.org/10.1103/PhysRevResearch.7.L022044

Abstract

We present a functional interpolation approach within the auxiliary master equation framework to efficiently and accurately solve correlated impurity problems in nonequilibrium dynamical mean-field theory (DMFT). By leveraging a near-exact auxiliary bath representation, the method estimates corrections via interpolation over a few bath realizations, significantly reducing computational cost and increasing accuracy. We illustrate the approach on the Anderson impurity model and on the Hubbard model within DMFT, capturing equilibrium and long-lived photodoped states.

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  61. k can, in principle, change as a function of n.
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  63. We do that by adding a random function (frand(ω)) to the physical hybridization function, ImΔdesR/Km=ImΔphysR/K+frandR/K(ω)∀m>1,where f is generated by choosing random values for the vertical axis between –0.3 and 0.3, at five equidistant points, between −ωmax and +ωmax, and interpolating between them. Notice that Δ̲desm may become unphysical, for example, noncausal. This is, however, not an issue, as the fit ensures that Δ̲auxm remains physical.
  64. In the sense that σtyp,Σ, i.e., the maximum over ω of the standard deviation of Σ̲, is less than 0.1 times the average over ω of Σ̲.
  65. By “plain” we mean without the FI improvement, corresponding to NT=1.
  66. See Supplemental Material at http://link.aps.org/supplemental/10.1103/PhysRevResearch.7.L022044 for details about our benchmark to determine the optimal values of the hyperparameters k and NT.
  67. The edges of the DOS are smoothed with a “fictitious” temperature 0.5Γ.
  68. The slight increases around ω=0 are because the FI scheme yields a noncausal self-energy, which is fixed by minimally adjusting the coefficients α to fulfill the constraint of causality; see Ref. [60].
  69. Consider that the self-energy assumes large values, leading to large absolute differences.
  70. D. Werner and E. Arrigoni, TU Graz repository, V1 https://repository.tugraz.at/records/fj52m-f8t04 (2025).

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Phys. Rev. Research 7, L022044– Published 29 May, 2025
  • Received 2 March 2025
  • Accepted 21 April 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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