High-performance functional renormalization group calculations for interacting fermions

TL;DR

This paper introduces a new computational scheme for functional Renormalization Group calculations on 2D fermionic systems, improving efficiency and scalability for complex multiband models.

Contribution

The authors develop a novel exchange parametrization fRG scheme with partition of unity insertions, enabling decoupling of propagators and enhanced computational performance.

Findings

Scheme achieves significant speedup on multi-core CPUs.

Fast convergence observed in Hubbard model calculations.

Method compares favorably with previous fRG approaches.

Abstract

We derive a novel computational scheme for functional Renormalization Group (fRG) calculations for interacting fermions on 2D lattices. 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 even in the case of complex multiband systems. 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. In most parameter areas, a fast convergence can be observed. Finally, we compare to previous results in order to relate our approach to other fRG studies.