Rigorous construction of ground state correlations in graphene: renormalization of the velocities and Ward Identities

TL;DR

This paper rigorously constructs the ground state correlations of the 2D Hubbard model on a honeycomb lattice, showing that interactions preserve the Fermi velocity's magnitude and isotropy while inducing charge velocity asymmetry, with no magnetic or superconducting instabilities.

Contribution

It provides a rigorous multiscale expansion for the ground state of the 2D Hubbard model on graphene, clarifying the effects of interactions on velocities and symmetries.

Findings

Fermi velocity remains close to non-interacting value and isotropic.

Interaction causes asymmetry in charge velocities.

No magnetic or superconducting instabilities detected.

Abstract

We consider the 2D Hubbard model on the honeycomb lattice, as a model for single layer graphene with screened Coulomb interactions; at half filling and weak coupling, we construct its ground state correlations by a convergent multiscale expansion, rigorously excluding the presence of magnetic or superconducting instabilities or the formation of a mass gap. The Fermi velocity, which can be written in terms of a convergent series expansion, remains close to its non-interacting value and turns out to be isotropic. On the contrary, the interaction produces an asymmetry between the two components of the charge velocity, in contrast with the predictions based on relativistic or continuum approximations.