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Hierarchically parallelised functional Renormalisation Group

Scientific area

Quantum field theory in solid state physics, correlated electron systems.

Short description

During the last two decades, the functional renormalisation group has been increasingly applied to models of condensed matter systems. Various different cases have been and are being addressed and investigated, with a substantial focus on correlated electron systems. The method ultimately relies on the numerical treatment of potentially very large ordinary differential equations the treatment of which can become computationally extremely demanding or even unfeasible within small-scale computing environments.

In order to open further perspectives and provide a proof-of-concept, a custom fRG code was analysed and adapted to large-scale HPC computing architectures, aiming at a scaling behaviour which extends properly up to the full 28 racks of JUQUEEN.

hp-fRG3D scatter plot of the effective interaction in the spin channel for the 2D Hubbard Model (the colours represent the value of V_spin).


  • 458,752 cores on BlueGene/Q (JUQUEEN)

Strong scaling of hp-fRGThe scaling behaviour of hp-fRG on JUQUEEN, extending to the full system size of 458,752 cores.

Programming language and model

  • C/C++
  • MPI with OpenMP

Tested on platforms

  • BlueGene/Q
  • x86
  • Intel MIC (KNC and KNL)

Application developers and contact

Cross-sectional team Application Optimisation
Jülich Supercomputing Centre
Institute for Advanced Simulation
Forschungszentrum Jülich GmbH
52425 Jülich

(Text and images provided by the developers)









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