FM 05-09; arXiv:0901.4867; Phys. Rev. B 79, 201403(R) (2009)

Authors : Alessandro Giuliani, Vieri Mastropietro

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

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.

Keywords: Graphene, 2D Hubbard model, Dirac points, degenerate Fermi surface, renormalization group, zero temperature correlations, effective QED, Ward identities, charge velocity.

Alessandro Giuliani,
Dipartimento di Matematica,
Universita' di Roma Tre,
L.go S. Leonardo Murialdo 1, 00146 Roma, Italy
giuliani@mat.uniroma3.it

Vieri Mastropietro,
Dipartimento di Matematica,
Universita' di Roma Tor Vergata,
Viale della ricerca Scientifica, 00133 Roma, Italia
mastropi@mat.uniroma2.it