Honeycomb Hubbard Model at van Hove Filling II: Lower Bounds of the Self-Energy

TL;DR

This paper rigorously proves that the honeycomb Hubbard model at van Hove filling exhibits non-Fermi liquid behavior by establishing lower bounds on the second derivatives of the self-energy with respect to external momentum.

Contribution

It provides a mathematical proof that the honeycomb Hubbard model at van Hove filling is not a Fermi liquid, completing previous work with new lower bounds on the self-energy derivatives.

Findings

The model is proven to be a non-Fermi liquid.

Established lower bounds on the second derivatives of the self-energy.

Completes the mathematical characterization of the model's non-Fermi liquid behavior.

Abstract

In this paper we complete the proof that the honeycomb Hubbard model with renormalized chemical potential $\mu=1$ is {\it not} a Fermi liquid in the mathematically precise sense of Salmhofer, by establishing the necessary lower bounds for second derivatives of the self-energy w.r.t. the external momentum.