Better integrators for functional renormalization group calculations

The European Physical Journal B, vol. 95

Abstract

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

Authors 2

1. Jacob Beyer Aachen Institute for Theoretical Solid State Physics

   RWTH Aachen University · University of Würzburg · The University of Melbourne

   Affiliation as printed

   Institute for Theoretical Physics, University of Würzburg, Würzburg, 97074, Germany

   Institute for Theoretical Solid State Physics, RWTH Aachen University, Aachen, 52056, Germany

   School of Physics, University of Melbourne, Parkville, VIC 3010, Australia

2. Florian Goth

   University of Würzburg

   Affiliation as printed

   Institute for Theoretical Physics, University of Würzburg, Würzburg, 97074, Germany