The Hubbard model at half-filling, part III: the lower bound on the self-energy

TL;DR

This paper rigorously proves that the two-dimensional half-filled Hubbard model does not behave as a Fermi liquid by establishing a lower bound on a key derivative of the self-energy, advancing mathematical understanding of strongly correlated systems.

Contribution

It provides a rigorous mathematical proof that the Hubbard model at half-filling is not a Fermi liquid, completing previous work with a new lower bound on the self-energy derivative.

Findings

Hubbard model at half-filling is not a Fermi liquid

Established a lower bound on the second derivative of the self-energy

Advances mathematical understanding of strongly correlated electron systems

Abstract

We complete the proof that the two-dimensional Hubbard model at half-filling is not a Fermi liquid in the mathematically precise sense of Salmhofer, by establishing a lower bound on a second derivative in momentum of the first non-trivial self-energy graph.