https://doi.org/10.1140/epjb/s10051-022-00378-x
Regular Article - Computational Methods
Better integrators for functional renormalization group calculations
1
Institute for Theoretical Physics, University of Würzburg, 97074, Würzburg, Germany
2
Institute for Theoretical Solid State Physics, RWTH Aachen University, 52056, Aachen, Germany
3
School of Physics, University of Melbourne, VIC 3010, Parkville, Australia
c
tobias.mueller@physik.uni-wuerzburg.de
Received:
29
March
2022
Accepted:
5
July
2022
Published online:
25
July
2022
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 
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.
Jacob Beyer, Florian Goth and Tobias Müller contributed equally to this work.
© The Author(s) 2022
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