High-resolution functional renormalization group calculations for interacting fermions on the square lattice

We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices [1]. The scheme is based on the exchange parametrization fRG for the two-fermion interaction, with additional insertions of truncated partitions of unity. These insertions decouple the fermionic propagators from the exchange propagators and lead to a separation of the underlying equations. We demonstrate that this separation is numerically advantageous and may pave the way for refined, large-scale computational investigations. Furthermore, on the basis of speedup data gained from our implementation, it is shown that this new variant facilitates efficient calculations on a large number of multi-core CPUs. We apply the scheme to the $t$,$t'$ Hubbard model on a square lattice to analyze the convergence of the results with the bond length of the truncation of the partition of unity. Due to the computational performance of the implementation a high resolution in momentum space can be achieved, which allows for an analysis of long ranged interactions.\\ \ [1] J. Lichtenstein, D. S\'{a}nchez de la Pe\~{n}a, et al., \textit{ArXiv e-prints} (2016), arXiv:1604.06296.