Renormalization of the 2-point function of the Hubbard model at half-filling

TL;DR

This paper rigorously analyzes the two-dimensional Hubbard model at half-filling, proving its non-Fermi liquid behavior and establishing the conditions for analyticity in the coupling constant at finite temperature.

Contribution

It introduces a new two-particle irreducible expansion to study the self-energy and demonstrates the model's non-Fermi liquid, Luttinger liquid nature with mathematical rigor.

Findings

The model is not a Fermi liquid but a Luttinger liquid with logarithmic corrections.

Analyticity in the coupling constant holds within a specific radius depending on temperature.

The nature of 2D Fermi systems depends on the Fermi surface shape.

Abstract

We prove that the two dimensional Hubbard model at finite temperature T and half-filling is analytic in the coupling constant in a radius at least $c/(\log T)^2$. We also study the self-energy through a new two-particle irreducible expansion and prove that this model is not a Fermi liquid, but a Luttinger liquid with logarithmic corrections. The techniques used are borrowed from constructive field theory so the result is mathematically rigorous and completely non-perturbative. Together with earlier results on the existence of two dimensional Fermi liquids, this new result proves that the nature of interacting Fermi systems in two dimensions depends on the shape of the Fermi surface.