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Better integrators for functional renormalization group calculations

Author

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  • Jacob Beyer

    (University of Würzburg
    RWTH Aachen University
    University of Melbourne)

  • Florian Goth

    (University of Würzburg)

  • Tobias Müller

    (University of Würzburg)

Abstract

We analyze a variety of integration schemes for the momentum space functional renormalization group calculation with the goal of finding an optimized scheme. Using the square lattice $$t-t'$$ t - t ′ Hubbard model as a testbed we define and benchmark the quality. Most notably we define an error estimate of the solution for the ordinary differential equation circumventing the issues introduced by the divergences at the end of the FRG flow. Using this measure to control for accuracy we find a threefold reduction in number of required integration steps achievable by choice of integrator. We herewith publish a set of recommended choices for the functional renormalization group, shown to decrease the computational cost for FRG calculations and representing a valuable basis for further investigations. Graphic abstract

Suggested Citation

  • Jacob Beyer & Florian Goth & Tobias Müller, 2022. "Better integrators for functional renormalization group calculations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(7), pages 1-11, July.
    • Handle: RePEc:spr:eurphb:v:95:y:2022:i:7:d:10.1140_epjb_s10051-022-00378-x
    DOI: 10.1140/epjb/s10051-022-00378-x
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    References listed on IDEAS

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    1. Artur Karimov & Denis Butusov & Valery Andreev & Erivelton G. Nepomuceno, 2021. "Rational Approximation Method for Stiff Initial Value Problems," Mathematics, MDPI, vol. 9(24), pages 1-17, December.
    2. Jonas B. Profe & Dante M. Kennes, 2022. "TU $$^2$$ 2 FRG: a scalable approach for truncated unity functional renormalization group in generic fermionic models," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(3), pages 1-13, March.
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    Cited by:

    1. Carsten Honerkamp & Dante M. Kennes & Volker Meden & Michael M. Scherer & Ronny Thomale, 2022. "Recent developments in the functional renormalization group approach to correlated electron systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(12), pages 1-3, December.

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    1. Carsten Honerkamp & Dante M. Kennes & Volker Meden & Michael M. Scherer & Ronny Thomale, 2022. "Recent developments in the functional renormalization group approach to correlated electron systems," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 95(12), pages 1-3, December.

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