Universality of conductivity in interacting graphene

TL;DR

This paper rigorously proves that the a.c. conductivity in interacting graphene remains universal and unaffected by weak short-range interactions, using advanced mathematical techniques.

Contribution

It provides a rigorous proof that the universal conductivity in graphene is unaffected by weak interactions, employing Ward Identities and Renormalization Group methods.

Findings

Universal a.c. conductivity is unaffected by weak interactions.

Rigorous proof using Ward Identities and Renormalization Group.

No interaction corrections to conductivity at half filling.

Abstract

The Hubbard model on the honeycomb lattice describes charge carriers in graphene with short range interactions. While the interaction modifies several physical quantities, like the value of the Fermi velocity or the wave function renormalization, the a.c. conductivity has a universal value independent of the microscopic details of the model: there are no interaction corrections, provided that the interaction is weak enough and that the system is at half filling. We give a rigorous proof of this fact, based on exact Ward Identities and on constructive Renormalization Group methods.