Self-energy effects in functional renormalization group flows of the two-dimensional $t$-$t'$ Hubbard model away from van Hove filling

TL;DR

This paper investigates how fermionic self-energy influences the phase diagram and critical scales in the two-dimensional $t$-$t'$ Hubbard model using functional renormalization group methods, especially away from van Hove filling.

Contribution

It demonstrates that including fermionic self-energy effects alters magnetic phase boundaries and critical scales, highlighting their importance in accurate phase diagram determination.

Findings

Self-energy causes Fermi surface flattening near hot spots.

Magnetic phase boundaries shift due to self-energy effects.

Critical scales are significantly enhanced by self-energy.

Abstract

We study the impact of the fermionic self-energy on one-loop functional renormalization group flows of the two-dimensional $t$-$t'$ Hubbard model, with emphasis on electronic densities away from van Hove filling. In the presence of antiferromagnetic hot spots, antiferromagnetic fluctuations lead to a flattening of the Fermi surface, shift magnetic phase boundaries and significantly enhance critical scales. We trace back this effect to the presence of a magnetic first order transition. For some parameters, the first order character of the latter is reduced by self-energy effects. For reliably determining phase diagrams, the fermionic self-energy should thus be taken into account in functional renormalization group studies if scattering between hot spots is important.