Honeycomb Hubbard Model at van Hove Filling

Abstract

This paper is devoted to the rigorous study of the low temperature properties of the two-dimensional weakly interacting Hubbard model on the honeycomb lattice in which the renormalized chemical potential $\mu$ has been fixed such that the Fermi surface consists of a set of exact triangles. Using renormalization group analysis around the Fermi surface, we prove that this model is {\it not} a Fermi liquid in the mathematically precise sense of Salmhofer. The main result is proved in two steps. First we prove that the perturbation series for Schwinger functions as well as the self-energy function have non-zero radius of convergence when the temperature $T$ is above an exponentially small value, namely $T_0\sim \exp (-C|\lambda {|}^{-1/2})$. Then we prove the necessary lower bound for second derivatives of self-energy w.r.t. the external momentum and achieve the proof.

This paper and 2108.10415 are merged into a single paper. 74 pages. Accepted for publication in Communications in Mathematical Physics

References in corpus (8)

• Electric Field Effect in Atomically Thin Carbon Films
• The electronic properties of graphene
• Overdoping graphene beyond the van Hove singularity
• Introducing strong correlation effects into graphene by gadolinium intercalation
• How to Resum Feynman Graphs
• Singular Fermi Surfaces II. The Two--Dimensional Case
• A numerically exact study of Weyl superconductivity
• Singular Fermi Surfaces I. General Power Counting and Higher Dimensional Cases