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Parallel Adaptive Integration in High-Performance Functional Renormalization Group Computations

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High-Performance Scientific Computing (JHPCS 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10164))

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Abstract

The conceptual framework provided by the functional Renormalization Group (fRG) has become a formidable tool to study correlated electron systems on lattices which, in turn, provided great insights to our understanding of complex many-body phenomena, such as high-temperature superconductivity or topological states of matter. In this work we present one of the latest realizations of fRG which makes use of an adaptive numerical quadrature scheme specifically tailored to the described fRG scheme. The final result is an increase in performance thanks to improved parallelism and scalability.

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Notes

  1. 1.

    See Ref. [7] for a more detailed derivation and an example application of the scheme.

  2. 2.

    For a review of Clenshaw-Curtis and a comparison with Gauss quadrature rules we refer to the excellent review [13].

  3. 3.

    We use the conventional notation indicating with the capital symbol the integral (\(\varPhi \)) and with the corresponding small cap symbol (\(\phi \)) its integrand.

  4. 4.

    Notice that the fRG flow in the current setup starts at high \(\varOmega \) values and successively reduces this scale during the flow.

  5. 5.

    The granularity of the affinity is set to ’compact,core,1’.

References

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Acknowledgements

Financial support from the Jülich Aachen Research Alliance–High Performance Computing, and the Deutsche Forschungsgemeinschaft (DFG) through grants GSC 111, RTG 1995 and SPP 1459 is gratefully acknowledged. We are thankful to the Jülich Supercomputing Centre (JSC) for the computing time made available to perform the numerical tests. Special thanks to JSC Guest Student Programme which sponsored the research internship of one of the authors.

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Authors and Affiliations

  1. Institute for Theoretical Solid State Physics, RWTH Aachen University, 52074, Aachen, Germany

    Julian Lichtenstein & David Sánchez de la Peña

  2. Aachen Institute for Advanced Study in Computational Engineering Science, RWTH Aachen University, 52072, Aachen, Germany

    Jan Winkelmann & Edoardo Di Napoli

  3. Department of Mathematics, Faculty of Science, University of Zagreb, 10000, Zagreb, Croatia

    Toni Vidović

  4. Jülich Supercomputing Centre, Forschungszentrum Jülich GmbH, 52425, Jülich, Germany

    Edoardo Di Napoli

  5. JARA–HPC, 52425, Jülich, Germany

    Edoardo Di Napoli

Authors
  1. Julian Lichtenstein
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  2. Jan Winkelmann
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  3. David Sánchez de la Peña
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  4. Toni Vidović
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  5. Edoardo Di Napoli
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Corresponding author

Correspondence to Julian Lichtenstein .

Editor information

Editors and Affiliations

  1. Forschungszentrum Jülich, Jülich, Germany

    Edoardo Di Napoli

  2. Forschungszentrum Jülich, Jülich, Germany

    Marc-André Hermanns

  3. RWTH Aachen University, Aachen, Germany

    Hristo Iliev

  4. RWTH Aachen University, Aachen, Germany

    Andreas Lintermann

  5. Forschungszentrum Jülich, Jülich, Germany

    Alexander Peyser

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Lichtenstein, J., Winkelmann, J., Sánchez de la Peña, D., Vidović, T., Di Napoli, E. (2017). Parallel Adaptive Integration in High-Performance Functional Renormalization Group Computations. In: Di Napoli, E., Hermanns, MA., Iliev, H., Lintermann, A., Peyser, A. (eds) High-Performance Scientific Computing. JHPCS 2016. Lecture Notes in Computer Science(), vol 10164. Springer, Cham. https://doi.org/10.1007/978-3-319-53862-4_15

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  • DOI: https://doi.org/10.1007/978-3-319-53862-4_15

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  • Print ISBN: 978-3-319-53861-7

  • Online ISBN: 978-3-319-53862-4

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