The 2D Hubbard model on the honeycomb lattice

TL;DR

This paper rigorously analyzes the 2D Hubbard model on a honeycomb lattice, showing that weak interactions modify certain properties without inducing superconductivity or magnetism, using constructive fermionic renormalization group methods.

Contribution

It provides a rigorous, constructive analysis of the Hubbard model on a honeycomb lattice, demonstrating stability of the Dirac fermion behavior under weak interactions.

Findings

Interaction modifies Fermi velocity and wave function renormalization.

No superconducting or magnetic instabilities are induced by weak interactions.

Correlation functions satisfy a Ward Identity similar to massless Dirac fermions.

Abstract

We consider the 2D Hubbard model on the honeycomb lattice, as a model for a single layer graphene sheet in the presence of screened Coulomb interactions. At half filling and weak enough coupling, we compute the free energy, the ground state energy and we construct the correlation functions up to zero temperature in terms of convergent series; analiticity is proved by making use of constructive fermionic renormalization group methods. We show that the interaction produces a modification of the Fermi velocity and of the wave function renormalization without changing the asymptotic infrared properties of the model with respect to the unperturbed non-interacting case; this rules out the possibility of superconducting or magnetic instabilities in the ground state. We also prove that the correlations verify a Ward Identity similar to the one for massless Dirac fermions, up to asymptotically negligible corrections and a renormalization of the charge velocity.