Speaker
Description
The functional renormalisation group has played an important role in providing a tool for unbiased investigation of strongly correlated systems in condensed matter. To aid for a quantitative investigation, a full, yet efficient, momentum [4] and frequency [5] treatment of the vertex and the self-energy is needed. Such methods have been developed in [4] and [5] for local Hubbard interactions, but face challenges upon the introduction of more extended interactions.
We show how the extended interactions can be implemented in a multi-channel partially bosonised fRG flow equations [2, 1] (the so called Single Boson Exchange fRG flow equations), which nonetheless avoids bias resulting from the so called “Fierz ambiguity”. We find that even with extended interactions, the part of the vertex responsible for the multi-boson exchanges is quantitatively negligible - similar to what has been found for local interactions in [3]. This paves the road for the future investigation of extended Hubbard Models (in the form applicable to Moirė materials), and the effect of electron-phonon coupling.
Finally, we present an analysis of the extended Hubbard model on square and triangular geometries at van Hove fillings.
