Non-local exchange effects in zigzag edge magnetism of neutral graphene nanoribbons

We study the role of non-locality of exchange in a neutral zigzag graphene nanoribbon within the $\pi$-orbital unrestricted Hartree-Fock approximation. Within this theory we find that the magnetic features are further stabilized for both the intra-edge and inter-edge exchange compared to mean field theories of zigzag ribbon based on local exchange (like the Hubbard model or the ab-initio Local Density Approximation). The inter-edge exchange produces an enhancement of the band-gap of the magnetic ground-state solutions. The effect of this enhanced exchange on the edge states can not be satisfactorily achieved by a local interaction with renormalized parameters.