Quasi-particle functional Renormalisation Group calculations in the two-dimensional half-filled Hubbard model at finite temperatures

Abstract

We present a highly parallelisable scheme for treating functional Renormalisation Group equations which incorporates a quasi-particle-based feedback on the flow and provides direct access to real-frequency self-energy data. This allows to map out the boundaries of Fermi-liquid regimes and to study the effect of quasi-particle degradation near Fermi liquid instabilities. As a first application, selected results for the two-dimensional half-filled perfectly nested Hubbard model are shown.

Quasi-particle functional renormalisation group calculations in the two-dimensional t-t'-Hubbard model

“…The additional a priori prospect of this extension was a potential improvement at the quantitative level. Results for the reference case at half filling and perfect nesting indeed suggested such an improvement [24], in the sense that the scales at which instabilities appear moved closer to results from other methods, a tentative improvement compared to fRG treatments based on bare propagators. However, here we move away from this reference case and find somewhat unexpected additional variations already at a qualitative level under certain circumstances.…”

“…It imposes itself in the QP-fRG mainly for reasons of feasibility and is a priori justified at weak coupling since there is no frequency dependence in the bare model. It can however become relevant, up to a degree that it may invalidate the approach, as also discussed in the preceding work [24].…”

“…This work is a direct follow-up of a work in which the method was first applied, namely to the half-filled and perfectly nested case [24]. We keep the overlap with this initial work at a minimum, mostly focusing on additional aspects.…”

“…We will briefly recall model and method, to then treat a set of sample cases for which we present and discuss the results. We do also cover some matters which were not considered in [24], some of them in the appendix. The content is to a substantial degree quite technical in nature.…”

“…by the temperature flow and the interaction flow. Here, we use an extended version of the interaction flow method as a specific type of numerical treatment of fRG equations, first applied to the 2dHM in the particle-hole symmetric case at half filling in a previous work [24]. In a nutshell, it consists in a Z-factor-enhanced version of the original interaction flow method [11].…”