Fraboulet, K., Heinzelmann, S., Bonetti, P. M., Al-Eryani, A., Vilardi, D., Toschi, A., & Andergassen, S. (2022). Single-boson exchange functional renormalization group application to the two-dimensional Hubbard model at weak coupling. The European Physical Journal B, 95, Article 202. https://doi.org/10.1140/epjb/s10051-022-00438-2
Single boson exchange approach; Functional renormalization group; Hubbard model
We illustrate the algorithmic advantages of the recently introduced single-boson exchange (SBE) formulation for the one-loop functional renormalization group (fRG), by applying it to the two-dimensional Hubbard model on a square lattice. We present a detailed analysis of the fermion-boson Yukawa couplings and of the corresponding physical susceptibilities by studying their evolution with temperature and interaction strength, both at half filling and finite doping. The comparison with the conventional fermionic fRG decomposition shows that the rest functions of the SBE algorithm, which describe correlation effects beyond the SBE processes, play a negligible role in the weak-coupling regime above the pseudo-critical temperature, in contrast to the rest functions of the conventional fRG. Remarkably, they remain finite also at the pseudo-critical transition, whereas the corresponding rest functions of the conventional fRG implementation diverge. As a result, the SBE formulation of the fRG flow allows for a substantial reduction of the numerical effort in the treatment of the two-particle vertex function, paving a promising route for future multiboson and multiloop extensions.
Austrian Science Fund German Research Foundation (DFG) Grant No. 465199066
Project No. I 2794-N35 Research Unit FOR 5413/1 Project No. AN 815/6-1
Quantum Many-body Systems Physics: 50% Computational Materials Science: 50%